Wick and Anti-Wick Characterizations of Linear Operators on Spaces of Power Series Expansions

We study links between Wick, anti-Wick and analytic kernel operators on the Bargmann transform side. We consider classes of kernels, whose corresponding operators agree with the sets of linear and continuous operators on spaces of power series expansions, which are Bargmann images of Pilipović space...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2022-10, Vol.28 (5), Article 71
Main Author: Toft, Joachim
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Anti-Wick operators
Approximations and Expansions
Bargmann transform
Fourier Analysis
Gelfand-Shilov spaces
Kernels
Linear operators
Matematik
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Pilipovic spaces
Power series
Pseudo-differential operators
Series expansion
Signal,Image and Speech Processing
Toeplitz operators
Wick operators
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Summary:We study links between Wick, anti-Wick and analytic kernel operators on the Bargmann transform side. We consider classes of kernels, whose corresponding operators agree with the sets of linear and continuous operators on spaces of power series expansions, which are Bargmann images of Pilipović spaces. We show that in several situations, the sets of Wick and kernel operators with symbols and kernels in such classes agree. We also find suitable subclasses to these kernel classes, whose corresponding sets of Wick and anti-Wick operators agree. We also show ring, module and composition properties for such classes.
ISSN:1069-5869
1531-5851
1531-5851
DOI:10.1007/s00041-022-09944-4