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Bhimani, D. G. & Toft, J. (2025). Factorizations for quasi-Banach time-frequency spaces and Schatten classes. Indagationes mathematicae, 36(3), 838-879
Open this publication in new window or tab >>Factorizations for quasi-Banach time-frequency spaces and Schatten classes
2025 (English)In: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 36, no 3, p. 838-879Article in journal (Refereed) Published
Abstract [en]

We deduce factorization properties for Wiener amalgam spaces WLp,q, an extended family of modulation spaces M(omega, B), and for Schatten symbols s(p)(w) in pseudo-differential calculus under e. g. convolutions, twisted convolutions and symbolic products. Here M(omega, B) can be any quasi-Banach Orlicz modulation space. For example we show that WL1,r * WLp,q = WLp,q and WL1,r#s(p)(w) = s(p)(w) when r is an element of (0, 1], r _= p, q _ infinity. In particular we improve Rudin's identity L-1 * L-1 = L-1. (c) 2024 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).

Place, publisher, year, edition, pages
Elsevier BV, 2025
Keywords
Algebras, Approximation identity, Modulation spaces, Modules, Quasi-Banach spaces, Schatten–von Neumann, Wiener amalgam spaces
National Category
Algebra and Logic
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-138486 (URN)10.1016/j.indag.2024.09.005 (DOI)001479136000001 ()2-s2.0-105003167562 (Scopus ID)
Available from: 2025-05-13 Created: 2025-05-13 Last updated: 2025-05-26Bibliographically approved
Ratnakumar, P. K., Toft, J. & Vindas, J. (2025). Non-isometric translation and modulation invariant Hilbert spaces. Journal of Mathematical Analysis and Applications, 550(1), Article ID 129530.
Open this publication in new window or tab >>Non-isometric translation and modulation invariant Hilbert spaces
2025 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 550, no 1, article id 129530Article in journal (Refereed) Published
Abstract [en]

Let H be a Hilbert space, continuously embedded in S'(Rd), and which contains at least one non-zero element in S'(Rd). If there is a constant C0 > 0 such that ||ei❮· ,ε❯ f ( ·  -x)||HC0||f||H, fH, x, ε ∈ Rd, then we prove that H = L2(Rd), with equivalent norms.

Place, publisher, year, edition, pages
Elsevier, 2025
Keywords
Modulation spaces, Feichtinger's minimization principle
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-138121 (URN)10.1016/j.jmaa.2025.129530 (DOI)001464358800001 ()2-s2.0-105001598319 (Scopus ID)
Available from: 2025-04-22 Created: 2025-04-22 Last updated: 2025-05-05Bibliographically approved
Bonino, M., Coriasco, S., Petersson, A. & Toft, J. (2024). Fourier Type Operators on Orlicz Spaces and the Role of Orlicz Lebesgue Exponents. Mediterranean Journal of Mathematics, 21(8), Article ID 219.
Open this publication in new window or tab >>Fourier Type Operators on Orlicz Spaces and the Role of Orlicz Lebesgue Exponents
2024 (English)In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 21, no 8, article id 219Article in journal (Refereed) Published
Abstract [en]

We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz–Sobolev type spaces. In particular, we extend Hörmander’s improvement of Mihlin’s Fourier multiplier theorem to the framework of Orlicz spaces. We also show how Young functions Φ of the Orlicz spaces are linked to properties of certain Lebesgue exponents pΦ and qΦ emerged from Φ.

Place, publisher, year, edition, pages
Springer Nature, 2024
Keywords
42B35, 46A16, 46E30, Orlicz, Primary 35S05, Quasi-Banach, Quasi-Young functionals, Secondary 46F10
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-138339 (URN)10.1007/s00009-024-02735-9 (DOI)2-s2.0-85209750736 (Scopus ID)
Available from: 2025-05-20 Created: 2025-05-20 Last updated: 2025-05-20
Gumber, A., Rana, N., Toft, J. & Üster, R. (2024). Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces. Journal of Functional Analysis, 286(3), Article ID 110225.
Open this publication in new window or tab >>Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces
2024 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 286, no 3, article id 110225Article in journal (Refereed) Published
Abstract [en]

We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend well-known results in the literature. For example we generalize the classical result by Cordero and Nicola that if [Formula presented], pj,qj⩽q′,q⩽p and a∈Mp,q, then the pseudo-differential operator Op(a) is continuous from Mp to Mp. We also show that the entropy functional Eϕ possess suitable continuity properties on a suitable Orlicz modulation space MΦ satisfying Mp⊆MΦ⊆M2, though Eϕ is discontinuous on M2=L2. 

Place, publisher, year, edition, pages
Elsevier, 2024
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-126078 (URN)10.1016/j.jfa.2023.110225 (DOI)001112096400001 ()2-s2.0-85176240932 (Scopus ID)
Funder
Swedish Research Council, 2019-04890
Available from: 2023-12-20 Created: 2023-12-20 Last updated: 2024-10-23Bibliographically approved
Gröchenig, K., Pfeuffer, C. & Toft, J. (2024). Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators. Forum mathematicum, 36(5), 1201-1224
Open this publication in new window or tab >>Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators
2024 (English)In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 36, no 5, p. 1201-1224Article in journal (Refereed) Published
Abstract [en]

We extend the stability and spectral invariance of convolution-dominated matrices to the case of quasi-Banach algebras p < 1. As an application, we construct a spectrally invariant quasi-Banach algebra of pseudodifferential operators with non-smooth symbols that generalize Sj & ouml;strand's results.

Place, publisher, year, edition, pages
Walter de Gruyter, 2024
Keywords
Pseudodifferential operators, spectral invariance, modulation space, Wiener's lemma, off-diagonal decay matrices, Gabor frame
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-128697 (URN)10.1515/forum-2023-0212 (DOI)001134560200001 ()2-s2.0-85181522372 (Scopus ID)
Available from: 2024-04-09 Created: 2024-04-09 Last updated: 2024-09-13Bibliographically approved
Toft, J. & Gumber, A. (2023). Fourier characterizations of Pilipović spaces. Journal of Functional Analysis, 284(1), Article ID 109724.
Open this publication in new window or tab >>Fourier characterizations of Pilipović spaces
2023 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 284, no 1, article id 109724Article in journal (Refereed) Published
Abstract [en]

Let f be a function or distribution on Rd. We characterize Pilipovic space in terms of certain estimates of the involved functions and suitable choices of their fractional Fourier transforms. For the analysis we derive a multi-dimensional version of Phragmen-Lindelof's theorem.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Fractional Fourier transforms, Bargmann transform, Multi-dimensional, Phragmén-Lindelöf's theorem
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-117836 (URN)10.1016/j.jfa.2022.109724 (DOI)000888075000006 ()2-s2.0-85139837239 (Scopus ID)
Available from: 2022-12-09 Created: 2022-12-09 Last updated: 2023-03-27Bibliographically approved
Toft, J., Bhimani, D. G. & Manna, R. (2023). Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipovic and modulation spaces. Applied and Computational Harmonic Analysis, 67, Article ID 101580.
Open this publication in new window or tab >>Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipovic and modulation spaces
2023 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 67, article id 101580Article in journal (Refereed) Published
Abstract [en]

We give a proof of that harmonic oscillator propagators and fractional Fourier transforms are essentially the same. We deduce continuity properties and fix time estimates for such operators on modulation spaces, and apply the results to prove Strichartz estimates for such propagators when acting on Pilipovic and modulation spaces. Especially we extend some results by Balhara, Cordero, Nicola, Rodino and Thangavelu. We also show that general forms of fractional harmonic oscillator propagators are continuous on suitable Pilipovic spaces.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Pilopovic spaces, Modulation spaces, Wiener amalgam, Bargmann transform, Harmonic oscillator, Propagators, Strichartz estimates
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-124903 (URN)10.1016/j.acha.2023.101580 (DOI)001060974200001 ()2-s2.0-85168005470 (Scopus ID)
Available from: 2023-09-26 Created: 2023-09-26 Last updated: 2023-10-11Bibliographically approved
Toft, J. & Uster, R. (2023). Pseudo-differential operators on Orlicz modulation spaces. Journal of Pseudo-Differential Operators and Applications, 14(1), Article ID 6.
Open this publication in new window or tab >>Pseudo-differential operators on Orlicz modulation spaces
2023 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 14, no 1, article id 6Article in journal (Refereed) Published
Abstract [en]

We deduce continuity properties for pseudo-differential operators with symbols in quasi-Banach Orlicz modulation spaces when rely on other quasi-Banach Orlicz modulation spaces. In particular we extend some earlier results.

Place, publisher, year, edition, pages
Springer, 2023
Keywords
Orlicz, Quasi-banach, Quasi-young functionals
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-118748 (URN)10.1007/s11868-022-00492-5 (DOI)000898866700001 ()2-s2.0-85143779437 (Scopus ID)
Available from: 2023-01-26 Created: 2023-01-26 Last updated: 2023-05-03Bibliographically approved
Toft, J., Bhimani, D. G. & Manna, R. (2023). Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type. Analysis and Applications, 21(2), 453-495
Open this publication in new window or tab >>Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type
2023 (English)In: Analysis and Applications, ISSN 0219-5305, E-ISSN 1793-6861 , Vol. 21, no 2, p. 453-495Article in journal (Refereed) Published
Abstract [en]

We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand-Shilov distributions.We use these results to show that psi dos with amplitudes in suitable modulation spaces, agree with normal type psi dos whose symbols belong to (other) modulation spaces. In particular we extend earlier trace results for modulation spaces, to include quasi-Banach modulation spaces. We also apply our results to extend earlier results on Schatten-von Neumann and nuclear properties for psi dos with amplitudes in modulation spaces.

Place, publisher, year, edition, pages
World Scientific, 2023
Keywords
Modulation spaces, Gelfand-Shilov spaces, Wiener amalgam spaces, trace map, amplitude, pseudo-differential operators
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-116460 (URN)10.1142/S0219530522500063 (DOI)000848581500001 ()2-s2.0-85133917521 (Scopus ID)
Available from: 2022-09-20 Created: 2022-09-20 Last updated: 2023-05-16Bibliographically approved
Teofanov, N. & Toft, J. (2022). An Excursion to Multiplications and Convolutions on Modulation Spaces. In: Aron, R.M., Moslehian, M.S., Spitkovsky, I.M., Woerdeman, H.J. (Ed.), Operator and Norm Inequalities and Related Topics: (pp. 601-637). Springer
Open this publication in new window or tab >>An Excursion to Multiplications and Convolutions on Modulation Spaces
2022 (English)In: Operator and Norm Inequalities and Related Topics / [ed] Aron, R.M., Moslehian, M.S., Spitkovsky, I.M., Woerdeman, H.J., Springer, 2022, p. 601-637Chapter in book (Refereed)
Abstract [en]

We give a self-contained introduction to (quasi-)Banach modulation spaces of ultradistributions, and review results on boundedness for multiplications and convolutions for elements in such spaces. Furthermore, we use these results to study the Gabor product. As an example, we show how it appears in a phase-space formulation of the nonlinear cubic Schrödinger equation.

Place, publisher, year, edition, pages
Springer, 2022
Series
Trends in Mathematics, ISSN 2297-0215, E-ISSN 2297-024X
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-122756 (URN)10.1007/978-3-031-02104-6_18 (DOI)2-s2.0-85136228564 (Scopus ID)9783031021039 (ISBN)9783031021046 (ISBN)
Available from: 2023-06-27 Created: 2023-06-27 Last updated: 2023-08-14Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1921-8168

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