Boundedness of metaplectic Toeplitz operators and Weyl symbols
Functional Analysis
2023-05-31 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.2305.03948,
title = {Boundedness of metaplectic Toeplitz operators and Weyl symbols},
author = {Haoren Xiong},
journal= {arXiv preprint arXiv:2305.03948},
year = {2023}
}
Comments
An explicit example has been added in Section 6, comparing to the previous version