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arXiv · 2303.01558

Characterizing boundedness of metaplectic Toeplitz operators

Lewis Coburn·Michael Hitrik·Johannes Sjoestrand
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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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Lewis Coburn, Michael Hitrik, Johannes Sjoestrand. 2023-03-02. Characterizing boundedness of metaplectic Toeplitz operators. https://arxiv.org/abs/2303.01558

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