# Weyl symbols and boundedness of Toeplitz operators

## TL;DR

This paper investigates the boundedness of Toeplitz operators on the Bargmann space with symbols that are exponentials of quadratic polynomials, establishing a link between operator boundedness and Weyl symbol boundedness.

## Contribution

It demonstrates that for a class of Toeplitz operators, boundedness is equivalent to the boundedness of their Weyl symbols, providing new insights into operator analysis.

## Key findings

- Boundedness of Toeplitz operators is implied by Weyl symbol boundedness.
- Focus on symbols that are exponentials of inhomogeneous quadratic polynomials.
- Results contribute to understanding the operator-symbol correspondence in quantum analysis.

## Abstract

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.