Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity

Teofanov, Nenad; Toft, Joachim; Wahlberg, Patrik

doi:10.1016/j.matpur.2022.09.002

Journal de Mathématiques Pures et Appliquées

2022

DOI: 10.1016/j.matpur.2022.09.002

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Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity

Nenad Teofanov

Joachim Toft

Patrik Wahlberg

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2022

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

Toft

2022

J Fourier Anal Appl

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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.

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

Toft

2022

J Fourier Anal Appl

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Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity

Cited by 1 publication

References 25 publications

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

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

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