Characterizing boundedness of metaplectic Toeplitz operators
Functional Analysis
2023-03-06 v1 Complex Variables
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.
Cite
@article{arxiv.2303.01558,
title = {Characterizing boundedness of metaplectic Toeplitz operators},
author = {Lewis Coburn and Michael Hitrik and Johannes Sjoestrand},
journal= {arXiv preprint arXiv:2303.01558},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2205.08649