# Spectral properties of semi-classical Toeplitz operators

## TL;DR

This paper derives asymptotic spectral measure expansions for semi-classical Toeplitz operators, including symmetry considerations, and explores inverse spectral implications, advancing understanding of their spectral properties.

## Contribution

It provides the first asymptotic expansion of the spectral measure for semi-classical Toeplitz operators, including an equivariant version with symmetry group considerations.

## Key findings

- Asymptotic expansion of spectral measure in powers of 5
- Equivariant spectral measure expansion with torus symmetry
- Inverse spectral consequences discussed

## Abstract

The main results of this paper are an asymptotic expansion in powers of $\hbar$ for the spectral measure $\mu_\hbar$ of a semi-classical Toeplitz operator, $Q_\hbar$, and an equivariant version of this result when $Q_\hbar$ admits an $n$-torus as a symmetry group. In addition we discuss some inverse spectral consequences of these results.