Sequence space representations for translation-modulation invariant function and distribution spaces

Andreas Debrouwere; Lenny Neyt

doi:10.1007/s00041-022-09981-z

Sequence space representations for translation-modulation invariant function and distribution spaces

Andreas Debrouwere, Lenny Neyt

Mathematics-TW

Research output: Contribution to journal › Article › peer-review

Abstract

We provide sequence space representations for the test function space D_E and the distribution space DE′ associated to a Banach space E belonging to a broad class of translation-modulation invariant Banach spaces of distributions. The spaces D_E and DE′ generalize the classical Schwartz spaces DLp and DLp′, respectively. Our proof is based on Gabor frame characterizations of D_E and DE′, which are also established here and are of independent interest. We recover in a unified way some known sequence space representations as well as obtain several new ones.

Original language	English
Article number	87
Journal	Journal of Fourier Analysis and Applications
Volume	28
Issue number	6
DOIs	https://doi.org/10.1007/s00041-022-09981-z
Publication status	Published - Dec 2022

Bibliographical note

Funding Information:
L. Neyt gratefully acknowledges support by FWO-Vlaanderen through the postdoctoral Grant 12ZG921N

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.

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title = "Sequence space representations for translation-modulation invariant function and distribution spaces",

abstract = "We provide sequence space representations for the test function space DE and the distribution space DE′ associated to a Banach space E belonging to a broad class of translation-modulation invariant Banach spaces of distributions. The spaces DE and DE′ generalize the classical Schwartz spaces DLp and DLp′, respectively. Our proof is based on Gabor frame characterizations of DE and DE′, which are also established here and are of independent interest. We recover in a unified way some known sequence space representations as well as obtain several new ones.",

author = "Andreas Debrouwere and Lenny Neyt",

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AU - Neyt, Lenny

N1 - Funding Information: L. Neyt gratefully acknowledges support by FWO-Vlaanderen through the postdoctoral Grant 12ZG921N Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2022 Elsevier B.V., All rights reserved.

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N2 - We provide sequence space representations for the test function space DE and the distribution space DE′ associated to a Banach space E belonging to a broad class of translation-modulation invariant Banach spaces of distributions. The spaces DE and DE′ generalize the classical Schwartz spaces DLp and DLp′, respectively. Our proof is based on Gabor frame characterizations of DE and DE′, which are also established here and are of independent interest. We recover in a unified way some known sequence space representations as well as obtain several new ones.

AB - We provide sequence space representations for the test function space DE and the distribution space DE′ associated to a Banach space E belonging to a broad class of translation-modulation invariant Banach spaces of distributions. The spaces DE and DE′ generalize the classical Schwartz spaces DLp and DLp′, respectively. Our proof is based on Gabor frame characterizations of DE and DE′, which are also established here and are of independent interest. We recover in a unified way some known sequence space representations as well as obtain several new ones.

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JF - Journal of Fourier Analysis and Applications

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ER -

Sequence space representations for translation-modulation invariant function and distribution spaces

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