On the Singular Values of Toeplitz Matrices

Abstract

In 1920 G. Szegö proved the basic result concerning the asymptotic distribution of the eigenvalues of selfadjoint Toeplitz matrices $T_n(f)$. An analogous result holds for the singular values in case $T_n(f)$ is not necessarily selfadjoint. In this paper we present a refinement of this (a second-order result) and also determine the limiting set of the singular values, both under appropriate hypotheses in the function $f$.