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Toft, J. (2019). Continuity of Gevrey-Hörmander pseudo-differential operators on modulation spaces. Journal of Pseudo-Differential Operators and Applications, 10(2), 337-358
Open this publication in new window or tab >>Continuity of Gevrey-Hörmander pseudo-differential operators on modulation spaces
2019 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 10, no 2, p. 337-358Article in journal (Refereed) Published
Abstract [en]

Let s ≥ 1, ω,ω ∈ P^0_{E,s} , a ∈ 􏰒\Gamma _s^(ω_0), and let B be a suitable invariant quasi-Banach function space. Then we prove that the pseudo-differential operator Op(a) is continuous from M(ω_0·ω, B) to M(ω, B).

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Pseudo-differential operators, Modulation spaces, BF-spaces, Gelfand–Shilov spaces
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-80298 (URN)10.1007/s11868-018-0273-9 (DOI)000466492500005 ()2-s2.0-85062799754 (Scopus ID)
Available from: 2019-02-07 Created: 2019-02-07 Last updated: 2019-08-29Bibliographically approved
Ivanenko, Y., Custafsson, M., Jonsson, B. L., Luger, A., Nilsson, B., Nordebo, S. & Toft, J. (2019). Passive Approximation and Optimization Using B-Splines. SIAM Journal on Applied Mathematics, 79(1), 436-458
Open this publication in new window or tab >>Passive Approximation and Optimization Using B-Splines
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2019 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 79, no 1, p. 436-458Article in journal (Refereed) Published
Abstract [en]

A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.

Keywords
approximation, Herglotz functions, B-splines, passive systems, convex optimization, sum rules
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-81228 (URN)10.1137/17M1161026 (DOI)000460127100021 ()2-s2.0-85063407473 (Scopus ID)
Available from: 2019-03-22 Created: 2019-03-22 Last updated: 2019-08-29Bibliographically approved
Abdeljawad, A., Cappiello, M. & Toft, J. (2019). Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting. Integral equations and operator theory, 91(3), Article ID UNSP 26.
Open this publication in new window or tab >>Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting
2019 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 91, no 3, article id UNSP 26Article in journal (Refereed) Published
Abstract [en]

We study some classes of pseudo-differential operators with symbols a admitting anisotropic exponential type growth at infinity. We deduce mapping properties for these operators on Gelfand-Shilov spaces. Moreover, we deduce algebraic and certain invariance properties of these classes.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Gevrey regularity, Symbols of infinite order, Gelfand-Shilov spaces, Short-time Fourier transform, Anisotropic
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-84519 (URN)10.1007/s00020-019-2518-2 (DOI)000467655500001 ()2-s2.0-85064002636 (Scopus ID)
Available from: 2019-06-05 Created: 2019-06-05 Last updated: 2019-08-29Bibliographically approved
Toft, J. (2019). Schatten properties, nuclearity and minimality of phase shift invariant spaces. Applied and Computational Harmonic Analysis, 46(1), 154-176
Open this publication in new window or tab >>Schatten properties, nuclearity and minimality of phase shift invariant spaces
2019 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 46, no 1, p. 154-176Article in journal (Refereed) Published
Abstract [en]

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.

We use these results to prove that the pseudo-differential operator Op(a) is a Schatten-q operator from M to Mp and r-nuclear operator from M to Mr when a∈Mr for suitable p, q and r in (0,∞].

Place, publisher, year, edition, pages
Elsevier, 2019
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61883 (URN)10.1016/j.acha.2017.04.003 (DOI)2-s2.0-85019043081 (Scopus ID)
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2019-08-29Bibliographically approved
Toft, J. (2019). Semi-continuous convolution estimates on weakly periodic Lebesgue spaces. In: Landscapes of Time-Frequency Analysis: . Paper presented at Aspects of Time–Frequency Analysis “ATFA17”, 5–7 June 2017, Torino (pp. 309-321). Springer
Open this publication in new window or tab >>Semi-continuous convolution estimates on weakly periodic Lebesgue spaces
2019 (English)In: Landscapes of Time-Frequency Analysis, Springer, 2019, p. 309-321Conference paper, Published paper (Refereed)
Abstract [en]

We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue quasi-norms are applied on the period instead of the whole axes. © Springer Nature Switzerland AG 2019.

Place, publisher, year, edition, pages
Springer, 2019
Series
Applied and Numerical Harmonic Analysis, ISSN 2296-5009, E-ISSN 2296-5017
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82758 (URN)10.1007/978-3-030-05210-2_13 (DOI)2-s2.0-85061324431 (Scopus ID)978-3-030-05209-6 (ISBN)978-3-030-05210-2 (ISBN)
Conference
Aspects of Time–Frequency Analysis “ATFA17”, 5–7 June 2017, Torino
Note

Export Date: 22 May 2019; Book Chapter

Available from: 2019-05-27 Created: 2019-05-27 Last updated: 2019-08-29Bibliographically approved
Chen, Y., Toft, J. & Wahlberg, P. (2019). The Weyl product on quasi-Banach modulation spaces. Bulletin of Mathematical Sciences, 9(2), 1-30, Article ID 1950018.
Open this publication in new window or tab >>The Weyl product on quasi-Banach modulation spaces
2019 (English)In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615, Vol. 9, no 2, p. 1-30, article id 1950018Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
World Scientific, 2019
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics; Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-70220 (URN)10.1142/S1664360719500188 (DOI)000481998100005 ()
Available from: 2018-01-29 Created: 2018-01-29 Last updated: 2019-09-24Bibliographically approved
Pilipovic, S. & Toft, J. (2019). Wave-front sets related to quasi-analytic Gevrey sequences. Publications de l'Institut Mathématique (Beograd), 105(119), 1-16
Open this publication in new window or tab >>Wave-front sets related to quasi-analytic Gevrey sequences
2019 (English)In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 105, no 119, p. 1-16Article in journal (Refereed) Published
Abstract [en]

Quasi-analytic wave-front sets of distributions which correspond to the Gevrey sequence p!(s), s is an element of [1/2, 1) are defined and investigated. The propagation of singularities are deduced by considering sequences of Gaussian windowed short-time Fourier transforms of distributions which are modifications of the original distributions by suitable restriction-extension techniques. Basic micro-local properties of the new wave-fronts are thereafter established.

Place, publisher, year, edition, pages
Publications de l'Institut Mathématique, 2019
Keywords
wave-front sets, ultradistributions
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-86922 (URN)10.2298/PIM1919001P (DOI)000472506500001 ()2-s2.0-85066126756 (Scopus ID)
Available from: 2019-07-18 Created: 2019-07-18 Last updated: 2019-08-29Bibliographically approved
Chen, Y., Signahl, M. & Toft, J. (2018). Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovic' kernels. Journal of Fourier Analysis and Applications, 24(3), 666-698
Open this publication in new window or tab >>Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovic' kernels
2018 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 24, no 3, p. 666-698Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
matrices, harmonic oscillator, Hermite functions, kernel theorems, Schatten-von Neumann operators, singular values
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61880 (URN)10.1007/s00041-017-9542-x (DOI)000432208800003 ()2-s2.0-85017414475 (Scopus ID)
Projects
Matematisk modellering, ICMM
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2019-08-29Bibliographically approved
Toft, J. & Nabizadeh Morsalfard, E. (2018). Periodic distributions and periodic elements in modulation spaces. Advances in Mathematics, 323, 193-225
Open this publication in new window or tab >>Periodic distributions and periodic elements in modulation spaces
2018 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 323, p. 193-225Article in journal (Refereed) Published
Abstract [en]

We characterize periodic elements in Gevrey classes, Gelfand-Shilov distribution spaces and modulation spaces, in terms of estimates of involved Fourier coefficients, and by estimates of their short-time Fourier transforms. If q is an element of [1, infinity), omega is a suitable weight and (epsilon(E)(0))' is the set of all E -periodic elements, then we prove that the dual of M-(omega)(infinity,q) boolean AND (epsilon(E)(0))' equals M-(1/omega)(infinity,q)' boolean AND (epsilon(E)(0))' by suitable extensions of Bessel's identity. (C) 2017 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Academic Press, 2018
Keywords
Fourier coefficients, Periodic, Ultradistribution, Gevrey classes, Gelfand-Shilov spaces
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-69760 (URN)10.1016/j.aim.2017.10.040 (DOI)000417885800006 ()2-s2.0-85033594269 (Scopus ID)
Available from: 2018-01-12 Created: 2018-01-12 Last updated: 2019-08-29Bibliographically approved
Toft, J. (2017). Continuity and compactness for pseudo-differential operators with symbols in quasi-Banach spaces or Hörmander classes. Analysis and Applications, 15(3), 353-389
Open this publication in new window or tab >>Continuity and compactness for pseudo-differential operators with symbols in quasi-Banach spaces or Hörmander classes
2017 (English)In: Analysis and Applications, ISSN 0219-5305, Vol. 15, no 3, p. 353-389Article in journal (Refereed) Published
Abstract [en]

We deduce continuity and Schatten–von Neumann properties for operators with matrices satisfying mixed quasi-norm estimates with Lebesgue and Schatten parameters in (0, ∞]. We use these results to deduce continuity and Schatten–von Neumann properties for pseudo-differential operators with symbols in quasi-Banach modulation spaces, or in appropriate H ̈ormander classes. 

Place, publisher, year, edition, pages
World Scientific, 2017
Keywords
Schatten-von Neumann, quasi-Banach, modulation spaces, Hörmander classes, matrices.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61873 (URN)10.1142/S0219530516500159 (DOI)000399796600003 ()2-s2.0-84983044987 (Scopus ID)
Projects
Matematisk modellering, ICMM
Note

Tillgänglig online sedan år 2016

Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2019-08-29Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1921-8168

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