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Extreme individual eigenvalues for a class of large Hessenberg Toeplitz matrices

  • J. M. Bogoya
  • S. M. Grudsky
  • I. S. Malysheva
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)

Abstract

In a previous work we studied the asymptotic behavior of individual inner eigenvalues of the n-by-n truncations of a certain family of infinite Hessenberg Toeplitz matrices as n goes to infinity. In the present work we deal with the extreme eigenvalues. The generating function of the Toeplitz matrices is supposed to be of the form \( a(t)\,= \, \frac{1}{t}(1\,-\,t)^{\alpha} f(t)\,\,(t\,\in\,\mathbb{T})\), where 0 < α < 1 and f is a smooth function in H

Keywords

Toeplitz matrix eigenvalue Fourier integral asymptotic expansion 

Mathematics Subject Classification (2010)

Primary 47B35 Secondary 15A15 15A18 47N50 65F15 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • J. M. Bogoya
    • 1
  • S. M. Grudsky
    • 2
  • I. S. Malysheva
    • 3
  1. 1.Pontificia Universidad JaverianaDepartamento de MatemáticasBogotáColombia
  2. 2.CINVESTAV del I.P.N., Departamento de MatemáticasApartado Postal 14-740Ciudad de MéxicoMéxico
  3. 3.Southern Federal University, Mathematics departmentRostov-on-DonRussia

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