Extreme individual eigenvalues for a class of large Hessenberg Toeplitz matrices

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


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


Toeplitz matrix eigenvalue Fourier integral asymptotic expansion 

Mathematics Subject Classification (2010)

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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • J. M. Bogoya
    • 1
    Email author
  • 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

Personalised recommendations