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Operator Algebras, Operator Theory and Applications pp 207–228Cite as

Higher-order Asymptotic Formulas for Toeplitz Matrices with Symbols in Generalized Hölder Spaces

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 181))

Abstract

We prove higher-order asymptotic formulas for determinants and traces of finite block Toeplitz matrices generated by matrix functions belonging to generalized Hölder spaces with characteristic functions from the Bari-Stechkin class. We follow the approach of Böttcher and Silbermann and generalize their results for symbols in standard Hölder spaces.

The author is supported by F.C.T. (Portugal) grants SFRH/BPD/11619/2002 and FCT/FEDER/POCTI/MAT/59972/2004.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    Alexei Yu. Karlovich

Authors
  1. Alexei Yu. Karlovich
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, U.T.L., Avenida Rovisco Pais, 1049-001, Lisboa, Portugal

    Maria Amélia Bastos , Amarino Brites Lebre  & Frank-Olme Speck ,  & 

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

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Karlovich, A.Y. (2008). Higher-order Asymptotic Formulas for Toeplitz Matrices with Symbols in Generalized Hölder Spaces. In: Bastos, M.A., Lebre, A.B., Speck, FO., Gohberg, I. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 181. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8684-9_10

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