Asymptotic formulas of Szegö–Kac–Achiezer type

Article type: Research Article

Authors: Gohberg, I. | Kaashoek, M.A.

Affiliations: Tel-Aviv University, Tel Aviv 69978, Israel | Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

Abstract: A generalization of Szegö's first limit theorem is deduced for a general class of block Toeplitz operators with Hilbert–Schmidt entries. Analogous formulas for Wiener–Hopf integral operators are derived, and by discretization a direct connection between the two types of asymptotics is established. For the continuous case the results are specified further for operators with a rational matrix symbol.

DOI: 10.3233/ASY-1992-5301

Journal: Asymptotic Analysis, vol. 5, no. 3, pp. 187-220, 1992