Opuscula Math. 40, no. 2 (2020), 241-270
https://doi.org/10.7494/OpMath.2020.40.2.241

 
Opuscula Mathematica

Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices

Ayoub Harrat
El Hassan Zerouali
Lech Zielinski

Abstract. We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.

Keywords: tridiagonal matrix, band matrix, unbounded self-adjoint operator, discrete spectrum, large eigenvalues, asymptotics.

Mathematics Subject Classification: 47B25, 47B36, 15A18.

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  • Ayoub Harrat
  • ORCID iD https://orcid.org/0000-0003-4029-4827
  • Center of Mathematical Research of Rabat, Department of Mathematics, Mohammed V University of Rabat, P.O. Box 1014, Marocco
  • Laboratoire de Mathématiques Pures et Appliquées, Joseph Liouville EA 2597, Université du Littoral Côtte d'Opale, F-62228 Calais, France
  • Lech Zielinski (corresponding author)
  • ORCID iD https://orcid.org/0000-0002-7314-7586
  • Laboratoire de Mathématiques Pures et Appliquées, Joseph Liouville EA 2597, Université du Littoral Côtte d'Opale, F-62228 Calais, France
  • Communicated by P.A. Cojuhari.
  • Received: 2020-01-13.
  • Revised: 2020-01-27.
  • Accepted: 2020-01-27.
  • Published online: 2020-03-09.
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Cite this article as:
Ayoub Harrat, El Hassan Zerouali, Lech Zielinski, Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices, Opuscula Math. 40, no. 2 (2020), 241-270, https://doi.org/10.7494/OpMath.2020.40.2.241

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