Characterizing Boundedness of Metaplectic Toeplitz Operators

Lewis Coburn; Michael Hitrik; Johannes Sjöstrand

doi:10.1093/imrn/rnad161

Characterizing Boundedness of Metaplectic Toeplitz Operators

Lewis Coburn
, Michael Hitrik
, Johannes Sjöstrand

Mathematics

University of California at Los Angeles
Université de Bourgogne

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger–Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.

Original language	English
Pages (from-to)	8264-8281
Number of pages	18
Journal	International Mathematics Research Notices
Volume	2024
Issue number	10
DOIs	https://doi.org/10.1093/imrn/rnad161
State	Published - May 1 2024

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abstract = "We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger–Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.",

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N2 - We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger–Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.

AB - We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger–Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.

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Characterizing Boundedness of Metaplectic Toeplitz Operators

Abstract

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