Spectral properties of semi-classical Toeplitz operators

Abstract

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