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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: 2024-01-11Bibliographically 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
Toft, J., Üster, R., Nabizadeh Morsalfard, E. & Öztop, S. (2022). Continuity properties and Bargmann mappings of quasi-Banach Orlicz modulation spaces. Forum mathematicum, 34(5), 1205-1232
Open this publication in new window or tab >>Continuity properties and Bargmann mappings of quasi-Banach Orlicz modulation spaces
2022 (English)In: Forum mathematicum, ISSN 0933-7741, E-ISSN 1435-5337, Vol. 34, no 5, p. 1205-1232Article in journal (Refereed) Published
Abstract [en]

We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces on R-d. We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.

Place, publisher, year, edition, pages
Walter de Gruyter, 2022
Keywords
Gabor analysis, Gelfand Shilov spaces, Pilipovic spaces, ultradistributions, Bargmann transform
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-116094 (URN)10.1515/forum-2021-0279 (DOI)000831351700001 ()2-s2.0-85135467675 (Scopus ID)
Available from: 2022-09-02 Created: 2022-09-02 Last updated: 2022-09-14Bibliographically approved
Teofanov, N., Toft, J. & Wahlberg, P. (2022). Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity. Journal des Mathématiques Pures et Appliquées, 167, 48-100
Open this publication in new window or tab >>Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity
2022 (English)In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, E-ISSN 1776-3371, Vol. 167, p. 48-100Article in journal (Refereed) Published
Abstract [en]

We study the link between ilidos and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short-time Fourier transform of the Weyl symbol. This gives characterizations of Wick symbols of ilidos of Shubin type and of infinite order, and results on composition. We prove a series expansion of Wick operators in terms of anti-Wick operators which leads to a sharp Garding inequality and transition of hypoellipticity between Wick and Shubin symbols. Finally we show continuity results for anti-Wick operators, and estimates for the Wick symbols of anti-Wick operators.(c) 2022 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Place, publisher, year, edition, pages
Elsevier, 2022
Keywords
Shubin symbols, Bargmann transform, Wick operators, Anti-Wick operators, Hypoellipticity, Gelfand-Shilov spaces
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-117486 (URN)10.1016/j.matpur.2022.09.002 (DOI)000875410900002 ()2-s2.0-85139730624 (Scopus ID)2022 (Local ID)2022 (Archive number)2022 (OAI)
Available from: 2022-11-11 Created: 2022-11-11 Last updated: 2022-12-13Bibliographically approved
Toft, J. (2022). Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces. Journal of Functional Analysis, 282(5), Article ID 109343.
Open this publication in new window or tab >>Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces
2022 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 282, no 5, article id 109343Article in journal (Refereed) Published
Abstract [en]

We prove boundedness of a general class of multipliers and Fourier multipliers, in particular of the Hilbert transform, when acting on quasi-Banach modulation spaces. We also deduce boundedness for multiplications and convolutions for elements in such spaces.

Place, publisher, year, edition, pages
Elsevier, 2022
Keywords
Hilbert transform, Convolutions, Multiplications
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-112953 (URN)10.1016/j.jfa.2021.109343 (DOI)000781808900009 ()2-s2.0-85120714456 (Scopus ID)2021 (Local ID)2021 (Archive number)2021 (OAI)
Available from: 2022-05-21 Created: 2022-05-21 Last updated: 2022-06-07Bibliographically approved
Toft, J. (2022). Wick and Anti-Wick Characterizations of Linear Operators on Spaces of Power Series Expansions. Journal of Fourier Analysis and Applications, 28(5), Article ID 71.
Open this publication in new window or tab >>Wick and Anti-Wick Characterizations of Linear Operators on Spaces of Power Series Expansions
2022 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 28, no 5, article id 71Article in journal (Refereed) Published
Abstract [en]

We study links between Wick, anti-Wick and analytic kernel operators on the Bargmann transform side. We consider classes of kernels, whose corresponding operators agree with the sets of linear and continuous operators on spaces of power series expansions, which are Bargmann images of Pilipovic spaces. We show that in several situations, the sets of Wick and kernel operators with symbols and kernels in such classes agree. We also find suitable subclasses to these kernel classes, whose corresponding sets of Wick and anti-Wick operators agree. We also show ring, module and composition properties for such classes.

Place, publisher, year, edition, pages
Springer, 2022
Keywords
Bargmann transform, Wick operators, Anti-Wick operators, Pseudo-differential operators, Toeplitz operators, Pilipovic spaces, Gelfand-Shilov spaces
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-116359 (URN)10.1007/s00041-022-09944-4 (DOI)000841801700001 ()2-s2.0-85136474656 (Scopus ID)
Available from: 2022-09-20 Created: 2022-09-20 Last updated: 2022-11-11Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1921-8168

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