Fourier characterizations of Pilipović spaces

Let f be a function or distribution on Rd. We characterize Pilipović 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 Phragmén-Lindelöf's theorem.

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Bibliographic Details
Published in:Journal of functional analysis 2023-01, Vol.284 (1), p.109724, Article 109724
Main Authors: Toft, Joachim, Gumber, Anupam
Format: Article
Language:English
Subjects:
Bargmann transform
Fractional Fourier transforms
Matematik
Mathematics
Multi-dimensional
Multi-dimensional Phragmén-Lindelöf's theorem
Phragmén-Lindelöf's theorem
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Summary:Let f be a function or distribution on Rd. We characterize Pilipović 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 Phragmén-Lindelöf's theorem.
ISSN:0022-1236
1096-0783
1096-0783
DOI:10.1016/j.jfa.2022.109724