Opuscula Mathematica
Opuscula Math. 40, no. 2 (2020), 241-270

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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About the authors ▼
Ayoub Harrat
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
El Hassan Zerouali
https://orcid.org/0000-0001-6240-7859
Center of Mathematical Research of Rabat, Department of Mathematics, Mohammed V University of Rabat, P.O. Box 1014, Marocco
Lech Zielinski (corresponding author)
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
About the article ▼
Communicated by P.A. Cojuhari.
Received: 2020-01-13.
Revised: 2020-01-27.
Accepted: 2020-01-27.
Published online: 2020-03-09.
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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