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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 12, Issue 3


Volume 13 (2015)

Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices

Anne Monvel
  • Institut de Mathématiques de Jussieu, Université Paris Diderot, bâtiment Sophie Germain, case 7012, 75205, Paris Cedex 13, France
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/ Lech Zielinski
  • LMPA, Centre Universitaire de la Mi-Voix, Université du Littoral, B.P. 699, 50 rue F. Buisson, 62228, Calais Cedex, France
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Published Online: 2013-12-21 | DOI: https://doi.org/10.2478/s11533-013-0348-z


We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.

MSC: 47B36; 47A10; 47A75; 15A42; 47A55

Keywords: Jacobi matrices; Eigenvalue estimates; Error estimates; Helffer-Sjöstrand formula

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About the article

Published Online: 2013-12-21

Published in Print: 2014-03-01

Citation Information: Open Mathematics, Volume 12, Issue 3, Pages 445–463, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0348-z.

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