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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 ()
Projects
Matematisk modellering, ICMM
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2018-07-11Bibliographically 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 ()
Available from: 2018-01-12 Created: 2018-01-12 Last updated: 2018-01-12Bibliographically approved
Chen, Y., Toft, J. & Wahlberg, P. (2018). The Weyl product on quasi-Banach modulation spaces. Bulletin of Mathematical Sciences
Open this publication in new window or tab >>The Weyl product on quasi-Banach modulation spaces
2018 (English)In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615Article in journal (Refereed) Epub ahead of print
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.

National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-70220 (URN)10.1007/s13373-018-0116-2 (DOI)
Available from: 2018-01-29 Created: 2018-01-29 Last updated: 2018-04-12
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 ()
Projects
Matematisk modellering, ICMM
Note

Tillgänglig online sedan år 2016

Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2018-05-21Bibliographically approved
Chen, Y., Signahl, M. & Toft, J. (2017). Hilbert space embeddings for Gelfand–Shilov and Pilipović spaces. In: Michael Oberguggenberger, Joachim Toft, Jasson Vindas, Patrik Wahlberg (Ed.), Michael Oberguggenberger, Joachim Toft, Jasson Vindas, Patrik Wahlberg (Ed.), Generalized Functions and Fourier Analysis: Dedicated to Stevan Pilipović on the Occasion of his 65th Birthday (pp. 31-44). Springer
Open this publication in new window or tab >>Hilbert space embeddings for Gelfand–Shilov and Pilipović spaces
2017 (English)In: Generalized Functions and Fourier Analysis: Dedicated to Stevan Pilipović on the Occasion of his 65th Birthday / [ed] Michael Oberguggenberger, Joachim Toft, Jasson Vindas, Patrik Wahlberg, Springer, 2017, p. 31-44Chapter in book (Refereed)
Abstract [en]

We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, H, and its dual, H′. We prove that for such quasi-Banach space B, there are convenient Hilbert spaces, Hk, k=1,2ss, with normalized Hermite functions as orthonormal bases and such that B lies between H1 and H1, and the latter spaces lie between H and H′.

Place, publisher, year, edition, pages
Springer, 2017
Series
Operator Theory: Advances and Applications ; 260
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-64652 (URN)10.1007/978-3-319-51911-1_3 (DOI)2-s2.0-85019068565 (Scopus ID)978-3-319-51910-4 (ISBN)978-3-319-51911-1 (ISBN)
Available from: 2017-06-02 Created: 2017-06-02 Last updated: 2017-06-27Bibliographically approved
Toft, J. (2017). Images of function and distribution spaces under the Bargmann transform. Journal of Pseudo-Differential Operators and Applications, 8(1), 83-139
Open this publication in new window or tab >>Images of function and distribution spaces under the Bargmann transform
2017 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 8, no 1, p. 83-139Article in journal (Refereed) Published
Abstract [en]

Weconsiderabroadfamilyoftestfunctionspacesandtheirdual(distribu- tion) spaces. The family includes Gelfand–Shilov spaces, and a family of test function spaces introduced by Pilipovic ́. We deduce different characterizations of such spaces, especially under the Bargmann transform and the Short-time Fourier transform. The family also include a test function space, whose dual space is mapped by the Bargmann transform bijectively to the set of entire functions. 

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Gelfand–Shilov estimates, Pilipovic ́ spaces, Ultradistributions, Bargmann transform
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61868 (URN)10.1007/s11868-016-0165-9 (DOI)000394537800005 ()
Projects
Matematisk modellering, ICMM
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2017-05-23Bibliographically approved
Ivanenko, Y., Gustafsson, M., Jonsson, B., Luger, A., Nilsson, B., Nordebo, S. & Toft, J. (2017). Passive approximation and optimization with B-splines.
Open this publication in new window or tab >>Passive approximation and optimization with B-splines
Show others...
2017 (English)Report (Other academic)
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 closed interval of the real axis. The approximating function is any Herglotz function with a generating measure that is absolutely continuous with Hölder continuous density in an arbitrary neighborhood of the approximation domain. The norm used is induced by any of the standard Lp-norms where 1 ≤ p ≤ ∞. The problem of interest is to study the convergence properties of simple Herglotz functions where the generating measures are given by finite B-spline expansions, and where the real part of the approximating functions are obtained via the Hilbert transform. In practice, such approximations are readily obtained as the solution to a finite- dimensional convex optimization problem. A constructive convergence proof is given in the case with linear B-splines, which is valid for all Lp-norms with 1 ≤ p ≤ ∞. A number of useful analytical expressions are provided regarding general B-splines and their Hilbert transforms. A typical physical application example is given regarding the passive approximation of a linear system having metamaterial characteristics. Finally, the flexibility of the optimization approach is illustrated with an example concerning the estimation of dielectric material parameters based on given dispersion data. 

Publisher
p. 24
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-63878 (URN)
Funder
Swedish Foundation for Strategic Research , AM13-0011
Available from: 2017-05-18 Created: 2017-05-18 Last updated: 2017-06-09Bibliographically approved
Cappiello, M. & Toft, J. (2017). Pseudo-differential operators in a Gelfand–Shilov setting. Mathematische Nachrichten, 290(5-6), 738-755
Open this publication in new window or tab >>Pseudo-differential operators in a Gelfand–Shilov setting
2017 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 5-6, p. 738-755Article in journal (Refereed) Published
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. 

Keywords
Pseudo-differential operators, Gelfand–Shilov spaces, short-time Fourier transform, modulation spaces
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61876 (URN)10.1002/mana.201500465 (DOI)000398384900008 ()
Projects
Matematisk modellering, ICMM
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2018-06-01Bibliographically approved
Toft, J. (2017). Schatten properties, nuclearity and minimality of phase shift invariant spaces. Applied and Computational Harmonic Analysis
Open this publication in new window or tab >>Schatten properties, nuclearity and minimality of phase shift invariant spaces
2017 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603XArticle in journal (Refereed) In press
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, 2017
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61883 (URN)10.1016/j.acha.2017.04.003 (DOI)
Available from: 2017-03-27 Created: 2017-03-27 Last updated: 2018-09-12
Fernandez, C., Galbis Verdu, A. & Toft, J. (2017). The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111(1), 1-13
Open this publication in new window or tab >>The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces
2017 (English)In: 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) Published
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.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Bargmann transform, Harmonic oscillator, Gelfand–Shilov spaces
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-50408 (URN)10.1007/s13398-015-0273-z (DOI)000392320300001 ()
Projects
Matematisk modellering
Available from: 2016-03-09 Created: 2016-03-09 Last updated: 2018-05-31Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1921-8168

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