Szegő limits for infinite Toeplitz matrices determined by the Taylor series of two rational functions

DOI10.1016/S0024-3795(01)00402-5zbMath0995.15020MaRDI QIDQ1348097

Alexander L. Sakhnovich

Publication date: 15 May 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Toeplitz operatorsinfinite Toeplitz matricesrational matrix functionsSzegő limits

Mathematics Subject Classification ID

Operator-theoretic methods (93B28) Hermitian, skew-Hermitian, and related matrices (15B57) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Matrices over function rings in one or more variables (15A54) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Cites Work

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• Some generalizations of Szegö's first limit theorem
• Szegö-Kac-Achiezer formulas in terms of realizations of the symbol
• Introduction to large truncated Toeplitz matrices
• Toeplitz matrices with an exponential growth of entries and the first Szegő limit theorem
• Toeplitz Matrices Generated by the Laurent Series Expansion of an Arbitrary Rational Function
• Formulas for the Evaluation of Toeplitz Determinants with Rational Generating Functions
• Toeplitz Operators with Piecewise Quasisectorial Symbols

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