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arXiv · 2305.03948

Boundedness of metaplectic Toeplitz operators and Weyl symbols

Haoren Xiong
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Abstract

We study Toeplitz operators on the Bargmann space, whose Toeplitz symbols are exponentials of complex inhomogeneous quadratic polynomials. Extending a result by Coburn--Hitrik--Sj\"{o}strand, we show that the boundedness of such Toeplitz operators implies the boundedness of the corresponding Weyl symbols, thus completing the proof of the Berger--Coburn conjecture in this case. We also show that a Toeplitz operator is compact precisely when its Weyl symbol vanishes at infinity in this case.

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Haoren Xiong. 2023-05-06. Boundedness of metaplectic Toeplitz operators and Weyl symbols. https://arxiv.org/abs/2305.03948

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