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Zeitschrift für Analysis und ihre Anwendungen


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Volume 26, Issue 1, 2007, pp. 43–56
DOI: 10.4171/ZAA/1309

Published online: 2007-03-31

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

Alexei Yu. Karlovich[1]

(1) Universidade Do Minho, Braga, Portugal

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.

Keywords: Block Toeplitz matrix, determinant, trace, weighted Wiener algebra, canonical Wiener–Hopf factorization, strong Szegö–Widom limit theorem

Karlovich Alexei: Asymptotics of Determinants and Traces of Toeplitz Matrices with Symbols in Weighted Wiener Algebras. Z. Anal. Anwend. 26 (2007), 43-56. doi: 10.4171/ZAA/1309