The Zak Transform on Gelfand–Shilov and Modulation Spaces with Applications to Operator Theory

We characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operat...

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Bibliographic Details
Published in:Complex analysis and operator theory 2021-02, Vol.15 (1), p.1, Article 2
Main Author: Toft, Joachim
Format: Article
Language:English
Subjects:
Analysis
Characterizations
Gelfand&#8211
Harmonic Analysis and Operator Theory
Linear operators
Matematik
Mathematics
Mathematics and Statistics
Modulation
Modulation spaces
Operator Theory
Periodic functions
Quasi-Banach spaces
Quasi-periodic
Shilov spaces
Wiener spaces
Zak transform
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Summary:We characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operators in order for these operators should be conjugations by Zak transforms.
ISSN:1661-8254
1661-8262
1661-8262
DOI:10.1007/s11785-020-01039-6