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Integral Equations and Operator Theory

, Volume 63, Issue 2, pp 165–180 | Cite as

The First Order Asymptotics of the Extreme Eigenvectors of Certain Hermitian Toeplitz Matrices

  • A. Böttcher
  • S. Grudsky
  • E. A. Maksimenko
  • J. Unterberger
Article

Abstract.

The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications. The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme eigenvectors of the matrices as their dimension increases to infinity.

Mathematics Subject Classification (2000).

Primary 47B35 Secondary 15A18, 41A80, 46N30 

Keywords.

Toeplitz matrix Fisher-Hartwig symbol eigenvalue eigenvector 

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Copyright information

© Birkhaueser 2009

Authors and Affiliations

  • A. Böttcher
    • 1
  • S. Grudsky
    • 2
  • E. A. Maksimenko
    • 2
  • J. Unterberger
    • 3
  1. 1.Fakultät für MathematikTU ChemnitzChemnitzGermany
  2. 2.Departamento de MatemáticasCINVESTAV del I.P.NMéxicoMéxico
  3. 3.Institut Élie CartanUniversité Henri Poincaré Nancy IVandœuvre-lès-Nancy CedexFrance

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