Spectral asymptotics for Toeplitz operators and an application to banded matrices

Abstract

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