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On the Structure of the Eigenvectors of Large Hermitian Toeplitz Band Matrices

  • Albrecht Böttcher
  • Sergei M. Grudsky
  • Egor A. Maksimenko
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)

Abstract

The paper is devoted to the asymptotic behavior of the eigenvectors of banded Hermitian Toeplitz matrices as the dimension of the matrices increases to infinity. The main result, which is based on certain assumptions, describes the structure of the eigenvectors in terms of the Laurent polynomial that generates the matrices up to an error term that decays exponentially fast. This result is applicable to both extreme and inner eigenvectors.

Mathematics Subject Classification (2000)

Primary 47B35 Secondary 15A18 41A25 65F15 

Keywords

Toeplitz matrix eigenvector asymptotic expansions 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  • Sergei M. Grudsky
    • 2
  • Egor A. Maksimenko
    • 2
  1. 1.Fakultät für MathematikTU ChemnitzChemnitzGermany
  2. 2.Departamento de MatemáticasCINVESTAV del I.P.N.MéxicoMéxico

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