Translation–Modulation Invariant Banach Spaces of Ultradistributions

We introduce and study a new class of translation–modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products; furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as wel...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2019-06, Vol.25 (3), p.819-841
Main Authors: Dimovski, Pavel, Pilipović, Stevan, Prangoski, Bojan, Vindas, Jasson
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Algebra
Approximations and Expansions
Banach spaces
Convolution
Fourier Analysis
Fourier transforms
Invariants
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Modulation
Modules
Multiplication
Partial Differential Equations
Signal,Image and Speech Processing
Tensors
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Summary:We introduce and study a new class of translation–modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products; furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as well as a Banach multiplication module structure over an associated Wiener–Beurling algebra. We also investigate a new class of modulation spaces, the Banach spaces of ultradistributions M F on R d , associated to translation–modulation invariant Banach spaces of ultradistributions F on R 2 d .
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-018-9610-x