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  • 1. Albeverioa, S.
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Shelkovichg,, V.M.
    The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 375, no 1, p. 82-98Article in journal (Refereed)
  • 2.
    Andersson, Anders
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    On the curvature of an inner curve in a Schwarz-Christoffel mapping2007Report (Other academic)
    Abstract [en]

    In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-­Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded.

    In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-­Christoffel mapping from R, the unit disk or upper half­plane, to a polygonal region P of a curve inside R. From the Schwarz-­Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

  • 3.
    Asano, Masanari
    et al.
    Tokuyama College of Technology, Japan.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science, Japan.
    Tanaka, Yoshiharu
    Tokyo University of Science, Japan.
    A hysteresis effect on optical illusion and non-Kolmogorovian probability theory2017In: White Noise Analysis and Quantum Information, World Scientific, 2017, Vol. 34, p. 201-213Chapter in book (Refereed)
    Abstract [en]

    In this study, we discuss a non-Kolmogorovness of the optical illusion in the human visual perception. We show subjects the ambiguous figure of "Schröeder stair", which has two different meanings [1]. We prepare 11 pictures which are inclined by different angles. The tendency to answer "left side is front" depends on the order of showing those pictures. For a mathematical treatment of such a context dependent phenomena, we propose a non-Kolmogorovian probabilistic model which is based on adaptive dynamics.

  • 4.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Brudnyi, Yuri
    Technion, Haifa, Israel.
    Interpolation of Multiparameter Approximation Spaces2004In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 129, no 2, p. 182-206Article in journal (Refereed)
  • 5. Asekritova, Irina
    et al.
    Kruglyak, Natan
    Elements of Functional Analysis in Problems1997Other (Other academic)
  • 6.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kruglyak, Natan
    Real Interpolation of Vector-Valued Spaces in Non-Diagonal Case2005In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 133, no 6, p. 1665-1675Article in journal (Refereed)
  • 7.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kruglyak, Natan
    The Besikovitch Covering Theorem and Near Minimizers for the Couple (L2,BV)2010In: Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, ISSN 1406-0086, E-ISSN 2228-0685, Vol. 59, no 1, p. 29-33Article in journal (Refereed)
  • 8.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kruglyak, Natan
    Maligranda, Lech
    Persson, Lars-Erik
    Distribution and Rearranement Estimates of the Maximal Functions and Interpolation1997In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 124, no 2, p. 107-132Article in journal (Refereed)
  • 9.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Kruglyak, Natan
    Nikolova, Ludmila
    Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation2005In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 170, no 3, p. 227-239Article in journal (Refereed)
  • 10.
    Asekritova, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Nikolova, Ludmila
    Sofia University, Sofia, Bulgaria.
    Kruglyak, Natan
    Luleå University of Technology, Luleå, Sweden.
    Maligranda, Lech
    Luleå University of Technology, Luleå, Sweden.
    Persson, Lars-Erik
    Luleå University of Technology, Luleå, Sweden.
    Lions-Peetre Reiteration Formulas for Triples and Their Application2001In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 145, no 3, p. 219-254Article in journal (Refereed)
  • 11.
    Berggren, Elin
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Sollervall, Håkan
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Searching for a sharp version of the Iliev-Sendov conjecture2010In: Advanced Studies in Contemporary Mathematics, ISSN 1229-3067, Vol. 20, no 1, p. 81-88Article in journal (Refereed)
  • 12.
    Boggiatto, Paolo
    et al.
    Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
    Oliaro, Alessandro
    Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
    Wahlberg, Patrik
    Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
    The wave front set of the Wigner distribution and instantaneous frequency2012In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 18, no 2, p. 410-438Article in journal (Refereed)
    Abstract [en]

    We prove a formula expressing the gradient of the phase function of a function f : R-d bar right arrow C as a normalized first frequency momentof the Wigner distribution for fixed time. The formula holds when f is the Fourier transform of a distribution of compact support, or when f belongs to a Sobolev space Hd/2+1+epsilon(R-d) where epsilon > 0. The restriction of the Wigner distribution to fixed time is well defined provided a certain condition on its wave front set is satisfied. Therefore we first need to study the wave front set of the Wigner distribution of a tempered distribution.

  • 13.
    Bölling, Kim
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Kronlund, Veronica
    Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Samarbete och glädje: - Ett sätt att försöka nå alla elever genom utematematik oavsett individuell förutsättning2015Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien är att ta reda på om och hur utematematik påverkar elevers inlärning. I studien ligger fokus på att upptäcka vilka effekter, som utematematik kan ge på alla elevers förståelse, oavsett individuell förutsättning. Då kring den egna kunskapen om och inlärningen av, ämnet matematik.Studien bygger på ett undervisningsförsök i en årskurs 3. Det matematiska innehållet är geometri, med inriktning på området omkrets. Sex stycken av eleverna som deltog i undervisningsförsöket med tillhörande observation, valdes ut och intervjuades efteråt.Resultatet visar att alla intervjuade elever beskriver att lektionen var givande på något sätt. Exempelvis berättar en elev i intervjun att hen nu fick ro att koncentrera sig eftersom hen fick mer frihet och utrymme att välja arbetsplats och avstånd till de andra eleverna, istället för att vara var låst till en specifik yta. Alla intervjuade elever uppvisar fördjupade kunskaper om vad omkrets innebär och hur denna mäts. Detta genom att beskriva och visa på olika objekts omkrets, både verbalt och med gester.

  • 14.
    Cappiello, Marco
    et al.
    Univ Turin.
    Rodino, Luigi
    Univ Turin.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Radial symmetric elements and the Bargmann transform2014In: Integral transforms and special functions, ISSN 1065-2469, E-ISSN 1476-8291, Vol. 25, no 9, p. 756-764Article in journal (Refereed)
    Abstract [en]

    We prove that a function or distribution on R^d is radial symmetric, if and only if its Bargmann transform is a composition by an entire function on C and the canonical quadratic function from C^d to C. 

  • 15.
    Cappiello, Marco
    et al.
    Universtiy of Torino, Italy.
    Schulz, René
    Leibniz Universität Hannover, Germany.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Conormal distributions in the Shubin calculus of pseudodifferential operators2018In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 2, article id 021502Article in journal (Refereed)
    Abstract [en]

    We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.

  • 16.
    Cappiello, Marco
    et al.
    University of Turin, Italy.
    Schulz, René
    Universität Hannover, Germany.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Shubin type Fourier integral operators and evolution equations2019In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999XArticle in journal (Refereed)
    Abstract [en]

    We study the Cauchy problem for an evolution equation of Schrödinger type. The Hamiltonian is the Weyl quantization of a real homogeneous quadratic form with a pseudodifferential perturbation of negative order from Shubin’s class. We prove that the propagator is a Fourier integral operator of Shubin type of order zero. Using results for such operators and corresponding Lagrangian distributions, we study the propagator and the solution, and derive phase space estimates for them.

  • 17.
    Cappiello, Marco
    et al.
    University of Turin, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pseudo-differential operators in a Gelfand–Shilov setting2017In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 5-6, p. 738-755Article in journal (Refereed)
    Abstract [en]

    We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes. 

  • 18.
    Carypis, Evanthia
    et al.
    University of Turin, Italy.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians2017In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 23, no 3, p. 530-571Article in journal (Refereed)
    Abstract [en]

    We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schrödinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are studied in the framework of projective Gelfand–Shilov spaces and their distribution duals. The corresponding notion of singularities is called the Gelfand–Shilov wave front set and means the lack of exponential decay in open cones in phase space. Our main result shows that the propagation is determined by the singular space of the quadratic form, just as in the framework of the Schwartz space, where the notion of singularity is the Gabor wave front set.

  • 19.
    Chen, Yuanyuan
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Signahl, Mikael
    University of Agder, Norway.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovic' kernels2018In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 24, no 3, p. 666-698Article in journal (Refereed)
    Abstract [en]

    We prove that any linear operator with kernel in a Pilipovi{\'c} or Gelfand-Shilov spacecan be factorized by two operators in the same class. We also give links onnumerical approximations for such compositions. We apply these composition rulesto deduce estimates of singular values and establish Schatten-von Neumann propertiesfor such operators.

  • 20.
    Chen, Yuanyuan
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    The Weyl product on quasi-Banach modulation spaces2019In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615, Vol. 9, no 2, p. 1-30, article id 1950018Article in journal (Refereed)
    Abstract [en]

    We study the bilinear Weyl product acting on quasi-Banach modulation spaces. We find sufficient conditions for continuity of the Weyl product and we derive necessary conditions. The results extend known results for Banach modulation spaces.

  • 21.
    Cordero, Elena
    et al.
    University of Turin.
    Tabacco, Anita
    Politecnico di Torino.
    Wahlberg, Patrik
    Università di Torino.
    Schrodinger-type propagators, pseudodifferential operators and modulation spaces2013In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 88, p. 375-395Article in journal (Refereed)
    Abstract [en]

    We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of non-degenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct, we obtain a characterization of all exponents p, q, r1, r2, t1, t2∈[1, ∞] of modulation spaces such that a symbol in Mp, q(ℝ2d) gives a pseudodifferential operator that is continuous from Mr1,r2(ℝd) into Mt1,t2(ℝd).

  • 22.
    Cordero, Elena
    et al.
    Turins universitet.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Sharp results for the Weyl product on modulation spaces2014In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 267, no 8, p. 3016-3057Article in journal (Refereed)
    Abstract [en]

    We give sufficient and necessary conditions on the Lebesgue exponentsfor the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to N=2 of aresult valid for the N-fold Weyl product. As a byproduct, we obtain sharpconditions for the twisted convolution to be bounded on Wieneramalgam spaces.

  • 23.
    Coriasco, Sandro
    et al.
    Department of mathematics, Turin's university, Italy.
    Johansson, Karoline
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Global wave front set of modulation space typeManuscript (preprint) (Other academic)
    Abstract [en]

    We introduce global wave-front sets WFB(f), f in S'(Rd), with respect to suitable Banach or Fréchet spaces B. An important special case is given by the modulation spaces B=M(ω,B), where ω is an appropriate weight function and B is a translation invariant Banach function space. We show that the standard properties for known notions of wave-front set extend to WFB(f). In particular, we prove that microlocality and microellipticity hold for a class of globally defined pseudo-differential operators Opt(a), acting continuouslyon the involved spaces.

  • 24.
    Coriasco, Sandro
    et al.
    Università degli Studi di Torino, Italy.
    Johansson, Karoline
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Global Wave-Front Properties for Fourier Integral Operators and Hyperbolic Problems2016In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, no 2, p. 285-333Article in journal (Refereed)
    Abstract [en]

    We illustrate the composition properties for an extended family of SG Fourier integral operators. We prove continuity results on modulation spaces, and study mapping properties of global wave-front sets for such operators. These extend classical results to more general situations. For example, there are no requirements on homogeneity for the phase functions. Finally, we apply our results to the study of the propagation of singularities, in the context of modulation spaces, for the solutions to the Cauchy problems for the corresponding linear hyperbolic operators. 

  • 25. Coriasco, Sandro
    et al.
    Johansson, Karoline
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Global wave-front sets of Banach, Fréchet and Modulation spacetypes, and pseudo-differential operators2013In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 254, no 8, p. 3228-3258Article in journal (Refereed)
    Abstract [en]

    We introduce global wave-front sets with respect to suitable Banach or Fréchet spaces. An important special case appears when choosing these spaces as modulation spaces. We show that the standard properties for known notions of wave-front set extend to global wave-front sets. In particular, we prove that microlocality and microellipticity hold for a class of globally defined pseudo-differential operators, acting continuously on the involved spaces.

  • 26.
    Coriasco, Sandro
    et al.
    Università degli Studi di Torino, Italy .
    Johansson, Karoline
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Global Wave-front Sets of Intersection and Union Type2014In: Fourier Analysis: Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations / [ed] Michael Ruzhansky, Ville Turunen, Heidelberg, New York, Dordrecht, London: Springer, 2014, p. 91-106Chapter in book (Refereed)
    Abstract [en]

    We show that a temperate distribution belongs to an ordered intersection or union of admissible Banach or Fréchet spaces if and only if the corresponding global wave-front set of union or intersection type is empty. We also discuss the situation where intersections and unions of sequences of spaces with two indices are involved. A main situation where the present theory applies is given by sequences of weighted, general modulation spaces.

  • 27.
    Coriasco, Sandro
    et al.
    Turin University, Italy.
    Johansson, Karoline
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators2013In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 169, no 3-4, p. 285-316Article in journal (Refereed)
    Abstract [en]

    Let ω, ω 0 be appropriate weight functions and ${\fancyscript{B}}$ be an invariant BF-space. We introduce the wave-front set ${{\rm WF}_{\mathcal{B}}(f)}$ with respect to the weighted Fourier Banach space ${\mathcal{B}=\fancyscript{F} \fancyscript{B}(\omega )}$ . We prove that the usual mapping properties for pseudo-differential operators Op t (a) with symbols a in ${S^{(\omega_0)}_{\rho, 0}}$ hold for such wave-front sets. In particular we prove ${{\rm WF}_{\mathcal C}({\rm Op}_t (a) f)\subseteq {\rm WF}_{\mathcal{B}}(f)}$ and ${{\rm WF}_{\mathcal{B}}(f) \subseteq {\rm WF} _{\mathcal C}({\rm Op}_t (a) f)\bigcup {\rm Char} (a)}$ . Here ${\mathcal{C}=\fancyscript{F} \fancyscript{B}(\omega /\omega_0)}$ and Char(a) is the set of characteristic points of a.

  • 28.
    Coriasco, Sandro
    et al.
    Università degli Studi di Torino, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    A calculus of Fourier integral operators with inhomogeneous phase functions on Rd2016In: Indian journal of pure and applied mathematics, ISSN 0019-5588, E-ISSN 0975-7465, Vol. 47, no 1, p. 125-166Article in journal (Refereed)
    Abstract [en]

    We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase func- tions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl-Hörmander calculus. We also prove the L^2(R^d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uni- formly bounded on R^{2d}.

  • 29.
    Coriasco, Sandro
    et al.
    Univ Turin, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Asymptotic expansions for Hörmander symbol classes in the calculus of pseudo-differential operators2014In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 5, no 1, p. 27-41Article in journal (Refereed)
    Abstract [en]

    We establish formulas for asymptotic expansions for S(m,g), the Hörmander class parameterized by the metric g and weight function m, defined on the phase space. By choosing m and g in appropriate ways, we cover some classical results on expansions for the standard symbol classes, and by choosing m and g in other ways we obtain asymptotic expansions for (generalized) SG classes.

  • 30.
    Engström, Christian
    et al.
    Umeå University, Sweden.
    Torshage, Axel
    Umeå University, Sweden.
    On equivalence and linearization of operator matrix functions with unbounded entries2017In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 89, no 4, p. 465-492Article in journal (Refereed)
    Abstract [en]

    In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of unbounded operator functions. Further, we deduce methods of finding equivalences to operator matrix functions that utilizes equivalences of the entries. Finally, a method of finding equivalences and linearizations to a general case of operator matrix polynomials is presented.

  • 31.
    Fernandez, Carmen
    et al.
    Universidad de Valencia.
    Galbis, Antonio
    Universidad de Valencia.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Spectral properties for matrix algebras2014In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 20, no 2, p. 362-383Article in journal (Refereed)
    Abstract [en]

    We consider Banach algebras of infinite matrices defined in terms of a weight measuring the off-diagonal decay of the matrix entries. If a given matrix A is invertible as an operator on l^2 we analyze the decay of its inverse matrix entries in the case where the matrix algebra is not inverse closed in B(l^2), the Banach algebra of bounded operators on l^2. To this end we consider a condition on sequences of weights which extends the notion of GRS-condition. Finally we focus on the behavior of inverses of pseudodifferential operators whose Weyl symbols belong to weighted modulation spaces and the weights lack the GRS condition.

  • 32.
    Fernandez, Carmen
    et al.
    University of Valencia, Spain.
    Galbis Verdu, Antonio
    University of Valencia, Spain.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces2017In: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, Vol. 111, no 1, p. 1-13Article in journal (Refereed)
    Abstract [en]

    We consider the counter images H_♭(R^d) and H_{0,♭}(R^d) of entire functions with exponential and almost exponential bounds, respectively, under the Bargmann transform, and we characterize them by estimates of powers of the harmonic oscillator. We also consider the Pilipovic ́ spaces S_s(R^d ) and Σ_s(R^d) when 0 < s < 1/2 and deduce their images under the Bargmann transform.

  • 33.
    Figueirinhas, Diogo
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    On the Properties of Gevreyand Ultra-analytic Spaces2016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    We look at the algebraic properties of Gevrey, analytic and ultraanalytic function spaces, namely their closure under composition, division and inversion. We show that both Gevrey and ultra-analytic spaces, G s with 1 ≤ s < ∞ and 0 < s < 1 respectively, form algebras. Closure under composition, division and inversion is shown to hold for the Gevrey case. For the ultra-analytic case we show it is not closed under composition. We also show that if a function is in G s , with 0 < s < 1 on a compact set, then it is in G s everywhere.

  • 34.
    Fredriksson, Henrik
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    On the Short-Time Fourier Transform and Gabor Frames generated by B-splines2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In this thesis we study the short-time Fourier transform. The short-time Fourier transform of a function f(x) is obtained by restricting our function to a short time segment and take the Fourier transform of this restriction. This method gives information locally of f in both time and frequency simultaneously.To get a smooth frequency localization one wants to use a smooth window, whichmeans that the windows will overlap.

    The continuous short-time Fourier transform is not appropriate for practical purpose, therefore we want a discrete representation of f. Using Gabor theory, we can write a function f as a linear combination of time- and frequency shifts of a fixed window function g with integer parameters a; b > 0. We show that if the window function g has compact support, then g generates a Gabor frame G(g; a; b). We also show that for such a g there exists a dual frame such that both G(g; a; b) and its dual frame has compact support and decay fast in the Fourier domain. Based on [2], we show that B-splines generates a pair of Gabor frames.

  • 35.
    Fredriksson, Henrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Wiener's lemma2013Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In this thesis we study Wiener’s lemma. The classical version of the lemma, whose realm is a Banach algebra, asserts that the pointwise inverse of a nonzero function with absolutely convergent Fourier expansion, also possesses an absolutely convergent Fourier expansion. The main purpose of this thesis is to investigate the validity inalgebras endowed with a quasi-norm or a p-norm.As a warmup, we prove the classical version of Wiener’s lemma using elemen-tary analysis. Furthermore, we establish results in Banach algebras concerning spectral theory, maximal ideals and multiplicative linear functionals and present a proof Wiener’s lemma using Banach algebra techniques. Let ν be a submultiplicative weight function satisfying the Gelfand-Raikov-Shilov condition. We show that if a nonzero function f has a ν-weighted absolutely convergent Fourier series in a p-normed algebra A. Then 1/f also has a ν-weightedabsolutely convergent Fourier series in A.

  • 36. Gröchenig, Karlheinz
    et al.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    The Range of Localization Operators and Lifting Theorems for Modulation and Bargmann-Fock Spaces2013In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 365, no 8, p. 4475-4496Article in journal (Refereed)
    Abstract [en]

    We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we characterize the range of certain Toeplitz operators on weighted Bargmann-Fock spaces. The main tools are the construction of canonical isomorphisms between modulation spaces of Hilbert-type and a refined version of the spectral invariance of pseudodifferential operators. On the technical level we prove a new class of inequalities for weighted gamma functions.

  • 37.
    Holst, Anders
    et al.
    1.Department of Mathematics Lund University 221 00 Lund, Sweden.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Wahlberg, Patrik
    3.School of Electrical Engineering and Computer Science University of Newcastle Callaghan, NSW 2308, Australia.
    Weyl product algebras and classical modulation spaces2010In: Linear and non-linear theory of generalized functions and its applications / [ed] A. Kaminski, M. Oberguggenberger, S. Pilipovic, Warsaw: Polish Acad. Sci. Inst. Math. , 2010, p. 153-158Conference paper (Refereed)
    Abstract [en]

    We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that M p,q   is an algebra under the Weyl product when p∈[1,∞]  and 1≤q≤min(p,p ′ )  .

  • 38.
    Håkansson, Christoffer
    et al.
    University of Kalmar, Kalmar Maritime Academy.
    Persson, Mikael
    University of Kalmar, Kalmar Maritime Academy.
    Motivation och livsstil till sjöss2008Independent thesis Basic level (professional degree), 5 poäng / 7,5 hpStudent thesis
    Abstract [sv]

    Vi som har författat detta arbete har riktat in oss på motivation till sjöss. Vad det är som

    lockar folk att gå till sjöss och hur upplever de aktiva sjömännen sin tillvaro ombord.

    Vi har gjort litteraturstudier för att samla in nödvändig fakta om motivation och livsstilar.

    Vi har även skickat enkäter till rederier för att se vad dom anser om utveklingen till sjöss.

    Vi har använt oss av en kvantitativ metod med enkät frågor riktade till aktiva sjömän,

    elever som utbildar sig på gymnasienivå till motorman/matros och rederier.

    I våran studie kom vi fram till att lönen anses vara ett problem när man skall rekrytera

    personal till svenska rederier. Den största faktorn som lockar människor till sjömansyrket

    är det fördelaktiga avlösningssystemet samt den långa sammanhängande ledigheten.

    För att få svenska sjömän att stanna kvar inom svensk sjöfart så måste näringen anstränga

    sig mer för att finna lösningar på problemet med att sjömän söker jobb på utländska

    rederier.

  • 39.
    Ivanenko, Yevhen
    et al.
    Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
    Nordebo, Sven
    Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
    Passive Approximation with High-Order B-Splines2019In: Analysis, Probability, Applications, and Computation / [ed] Karl‐Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Wahlberg, Birkhäuser Verlag, 2019, p. 83-94Conference paper (Refereed)
    Abstract [en]

    Convex optimization has emerged as a well-suited tool for passive approximation. Here, it is desired to approximate some pre-defined non-trivial system response over a given finite frequency band by using a passive system. This paper summarizes some explicit results concerning the Hilbert transform of general B-splines of arbitrary order and arbitrary partitions that can be useful with the convex optimization formulation. A numerical example in power engineering is included concerning the identification of some model parameters based on measurements on high-voltage insulation materials.

  • 40.
    Johansson, Karoline
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    A counter example on nontangential convergence for oscillatory integrals2010In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 87, no 101, p. 129-137Article in journal (Refereed)
    Abstract [en]

    Consider the solution of the time-dependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin (1989) that there exists f in the Sobolev space Hs(Rn), s=n/2 such that tangential convergence can not be widened to convergence regions. In this paper we show that the corresponding result holds when -Δx is replaced by an operator φ(D), with special conditions on φ.

  • 41.
    Johansson, Karoline
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Association between temperate distributions and analytical functions in the context of wave-front sets2011In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 2, no 1, p. 65-89Article in journal (Refereed)
    Abstract [en]

    Let B be a translation invariant Banach function space (BF-space). In this paper we prove that every temperate distribution f can be associated with a function F analytic in the convex tube Ω = {z in Cd; | Im z| < 1 } such that the wave-front set of f of Fourier BF-space types in intersection with Rd ×Sd-1 consists of the points (x, ξ) such that F does not belong to the Fourier BF-space at xi ξ.

  • 42.
    Johansson, Karoline
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Generalized free time-dependent Schrödinger equation with initial data in Fourier Lebesgue spaces2011In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 2, no 4, p. 543-556Article in journal (Refereed)
    Abstract [en]

    Consider the solution of the free time-dependent Schrödinger equation with initial data f. It is shown by Sjögren and Sjölin that there exists f in the Sobolev spaceHs (Rd ), s = d/2 such that tangential convergence can not be widened to convergence regions. The author obtained in a previous paper the corresponding results for a generalized version of the Schrödinger equation, where −Δx is replaced by an operator ϕ(D), with special conditions on ϕ. In this paper we show that similar results may be obtained for initial data in usual and mixed Fourier Lebesgue spaces. We also relax the conditions on ϕ.

  • 43.
    Johansson, Karoline
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Propagation of singularities for pseudo-differential operators and generalized Schrödinger propagators2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we discuss different types of regularity for distributions which appear in the theory of pseudo-differential operators and partial differential equations. Partial differential equations often appear in science and technology. For example the Schrödinger equation can be used to describe the change in time of quantum states of physical systems. Pseudo-differential operators can be used to solve partial differential equations.  They are also appropriate to use when modeling different types of problems within physics and engineering. For example, there is a natural connection between pseudo-differential operators and stationary and non-stationary filters in signal processing. Furthermore, the correspondence between symbols and operators when passing from classical mechanics to quantum mechanics essentially agrees with symbols and operators in the Weyl calculus of pseudo-differential operators.

    In this thesis we concentrate on investigating how regularity properties for solutions of partial differential equations are affected under the mapping of pseudo-differential operators, and in particular of the free time-dependent Schrödinger operators.

    The solution of the free time-dependent Schrödinger equation can be expressed as a pseudo-differential operator, with non-smooth symbol, acting on the initial condition. We generalize a result about non-tangential convergence, which was obtained by Sjögren and Sjölin (1989) for the free time-dependent Schrödinger equation.

    Another way to describe regularity for a distribution is to use wave-front sets. They do not only describe where the singularities are, but also the directions in which these singularities appear. The first types of wave-front sets (analytical wave-front sets) were introduced by Sato (1969, 1970). Later on Hörmander introduced ``classical'' wave-front sets (with respect to smoothness) and showed results in the context of pseudo-differential operators with smooth symbols, cf. Hörmander (1985).

    In this thesis we consider wave-front sets with respect to Fourier Banach function spaces. Roughly speaking, we take B as a Banach space, which is invariant under translations and embedded between the space of Schwartz functions and the space of temperated distributions. Then we say that the wave-front set of a distribution contains all points (x0, ξ0) such that no localization of the distribution at x0, belongs to FB in the direction ξ0. We prove that pseudo-differential operators with smooth symbols shrink the wave-front set and we obtain opposite embeddings by using sets of characteristic points of the operator symbols.

  • 44.
    Johansson, Karoline
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Properties of wave-front sets and non-tangential convergence2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we consider regularity properties for solutions to partial differential equations and pseudo-differential equations. The thesis mainly concerns wave-front sets and micro-local properties. Regularity properties are also viewed in terms of nontangential convergence for the generalized free time-dependent Schrödinger equations, where the Laplace operator is replaced by more general functions.

    Wave-front sets describe location of singularities and the directions of their propagation. We establish usual and convenient mapping properties for such wave-front sets under action of pseudodifferential operators with smooth symbols.

    We define three components of wave-front sets with respect to appropriate Banach and Fréchet spaces, in order to describe local properties as well as behavior far away, including heavy oscillations. The union of these components is called the global wavefront set. For these wave-front sets, we establish micro-local and micro-ellipticity properties for pseudo-differential operators in appropriate symbol classes. We obtain the classical wave-front sets as special cases (cf. Hörmander [9]). For the type of wave-front sets which describe local properties we also prove equivalence between wave-front sets of Fourier Banach function and modulation space types.

    To open up for numerical computations we introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier Lebesgue and modulation spaces. Furthermore, we prove that these wave-front sets agree with each other and with the corresponding wave-front sets of continuous type. We also consider the link between analytic functions and temperate distributions in terms of such wave-front sets.

    The last part of this thesis concerns counter examples of nontangential convergence for the generalized time-dependent Schrödinger equation with initial data in Sobolev spaces.

  • 45.
    Johansson, Karoline
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Coriasco, Sandro
    University of Torino, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Local wave-front sets of Banach and Fréchet types, with applications to pseudo-differential operatorsManuscript (preprint) (Other academic)
    Abstract [en]

    Let ω, ω0 be appropriate weight functions and B be an invariant BF-space. We introduce the wave-front set WFFB(ω)(f) with respect to weighted Fourier Banach space FB(ω). We prove the usual mapping properties for pseudo-differential operators Opt(a) with symbols a inS^{ω0}_{ρ,0} hold for such wave-front sets.

  • 46.
    Johansson, Karoline
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pilipovic, Stevan
    University of Novi Sad, Serbia .
    Teofanov, Nenad
    University of Novi Sad, Serbia .
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    A note on wave-front sets of Roumieu type ultradistributions2013In: Pseudo-Differential Operators, Generalized Functionsand Asymptotics / [ed] S. Molahajlo, S. Pilipovic, J. Toft, M. W. Wong, Basel Heidelberg NewYork Dordrecht London: Springer, 2013, p. 239-252Chapter in book (Refereed)
    Abstract [en]

    We study wave-front sets in weighted Fourier–Lebesgue spaces and corresponding spaces of ultradistributions. We give a comparison of these sets with the well-known wave-front sets of Roumieu type ultradistributions. Then we study convolution relations in the framework of ultradistributions. Finally, we introduce modulation spaces and corresponding wave-front sets, and establish invariance properties of such wave-front sets.

  • 47.
    Johansson, Karoline
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Pilipovic, Stevan
    Univ Novi Sad.
    Teofanov, Nenad
    Univ Novi Sad.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Gabor pairs, and a discrete approach to wave-front sets2012In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 166, no 2, p. 181-199Article in journal (Refereed)
    Abstract [en]

    We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of "continuous type". This implies that the coefficients of a Gabor frame expansion of $f$ are parameter dependent, and describe the wave-front set of $f$.

  • 48.
    Johansson, Karoline
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Pilipovic, Stevan
    Teofanov, Nenad
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Micro-local analysis in some spaces of ultradistributions2012In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 92, no 106, p. 1-24Article in journal (Refereed)
    Abstract [en]

    We extend some results from [14] and [19], concerning wave-front sets of Fourier–Lebesgue and modulation space types, to a broader class of spaces of ultradistributions. We relate these wave-front sets one to another and to the usual wave-front sets of ultradistributions.

    Furthermore, we give a description of discrete wave-front sets by intro- ducing the notion of discretely regular points, and prove that these wave-front sets coincide with corresponding wave-front sets in [19]. Some of these inves- tigations are based on the properties of the Gabor frames.

  • 49.
    Johansson, Karoline
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pilipovic, Stevan
    University of Novi Sad, Serbia.
    Teofanov, Nenad
    University of Novi Sad, Serbia.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Resolution of the wave- front set via discrete sets2013In: Proceedings in Applied Mathematics and Mechanics: PAMM, ISSN 1617-7061, E-ISSN 1617-7061, Vol. 13, p. 495-496Article in journal (Refereed)
    Abstract [en]

    We introduce discrete wave-front sets of sup type and prove that they coincide with the Hörmander wave-front set of a distribution. To that end we recall the notion of admissible lattice pairs and wave-front sets in Fourier-Lebesgue spaces.

  • 50.
    Kasana, H. S.
    et al.
    Thapar Institute of Engineering and Technology, India.
    Sollervall, Håkan
    Uppsala University, Sweden.
    Approximation of unbounded functions by linear positive operators1996In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 180, no 1, p. 85-93Article in journal (Refereed)
123 1 - 50 of 133
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