Asymptotics of Determinants and Traces of Toeplitz Matrices with Symbols in Weighted Wiener Algebras

Abstract

We prove asymptotic formulas for determinants and traces of finite block Toeplitz matrices with symbols belonging to Wiener algebras with weights satisfying natural submultiplicativity, monotonicity, and regularity conditions. The remainders in these formulas depend on the weights and go rapidly to zero for very smooth symbols. These formulas refine or extend some previous results by Szegö, Widom, Böttcher, and Silbermann.