Spectral asymptotics for a class of Toeplitz operators on the Bergman space

TL;DR

This paper analyzes the asymptotic behavior of singular values for a specific class of Toeplitz operators on the Bergman space, revealing new spectral properties related to boundary behavior.

Contribution

It provides the first detailed asymptotic analysis of singular values for Toeplitz operators with boundary-regular symbols on the Bergman space.

Findings

Asymptotic formulas for singular values of Toeplitz operators

Extension of results to banded matrices

Insights into spectral properties near the boundary

Abstract

We consider a class of compact Toeplitz operators on the Bergman space on the unit disk. The symbols of operators in our class are assumed to have a sufficiently regular power-like behaviour near the boundary of the disk. We compute the asymptotics of singular values of this class of Toeplitz operators. We use this result to obtain the asymptotics of singular values for a class of banded matrices.