Translation and modulation invariant Hilbert spaces

Let H be a Hilbert space of distributions on R d which contains at least one non-zero element of the Feichtinger algebra S 0 and is continuously embedded in D ′ . If H is translation and modulation invariant, also in the sense of its norm, then we prove that H = L 2 , with the same norm apart from a...

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Bibliographic Details
Published in:Monatshefte für Mathematik 2021-10, Vol.196 (2), p.389-398
Main Authors: Toft, Joachim, Gumber, Anupam, Manna, Ramesh, Ratnakumar, P. K.
Format: Article
Language:English
Subjects:
Feichtinger's minimization principle
Hilbert space
Invariants
Matematik
Mathematics
Mathematics and Statistics
Modulation
Modulation spaces
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Summary:Let H be a Hilbert space of distributions on R d which contains at least one non-zero element of the Feichtinger algebra S 0 and is continuously embedded in D ′ . If H is translation and modulation invariant, also in the sense of its norm, then we prove that H = L 2 , with the same norm apart from a multiplicative constant.
ISSN:0026-9255
1436-5081
1436-5081
DOI:10.1007/s00605-021-01589-7