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Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra

  • Albrecht Böttcher
  • Sergei Grudsky
Part of the Operator Theory: Advances and Applications book series (OT, volume 199)

Abstract

Sequences of so-called variable-coefficient Toeplitz matrices arise in many problems, including the discretization of ordinary differential equations with variable coefficients. Such sequences are known to be bounded if the generating function satisfies a condition of the Wiener type, which is far away from the minimal requirement in the case of constant coefficients. The purpose of this paper is to uncover some phenomena beyond the Wiener condition. We provide counterexamples on the one hand and prove easy-to-check sufficient conditions for boundedness on the other.

Mathematics Subject Classification (2000)

Primary 47B35 Secondary 15A60 65F35. 

Keywords

Toeplitz matrix variable coefficients matrix norm 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  • Sergei Grudsky
    • 2
  1. 1.Fakultät für MathematikTU ChemnitzChemnitzGermany
  2. 2.Departamento de MatemáticasCINVESTAV del I.P.N.México, D.F.México

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