On sum rules of special form for Jacobi matrices

Stanislav Kupin

doi:10.1016/S1631-073X(03)00132-8

Mathematical Physics

On sum rules of special form for Jacobi matrices
[Sur des règles de sommation pour des matrices de Jacobi]

Présenté par : Pierre-Louis Lions

Stanislav Kupin ¹

¹ Department of Mathematics, Box 1917, Brown University, Providence, RI 02912, USA

Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 611-614.

Résumé
Abstract

Nous appliquons les règles de sommation de Case à l'étude de propriétés spectrales de matrices de Jacobi d'un certain type. Nous obtenons un analogue discret d'un résultat de Molchanov, Novitskii and Vainberg (Comm. Math. Phys. 216 (2001) 195–213) comme un des corollaires du théorème principal.

We use sum rules of a special form to study spectral properties of Jacobi matrices. As a consequence of the main theorem, we obtain a discrete counterpart of a result by Molchanov, Novitskii and Vainberg (Comm. Math. Phys. 216 (2001) 195–213).

Reçu le : 2003-01-29
Accepté le : 2003-03-03
Publié le : 2003-04-01

DOI : 10.1016/S1631-073X(03)00132-8

Affiliations des auteurs :

Stanislav Kupin ¹

¹ Department of Mathematics, Box 1917, Brown University, Providence, RI 02912, USA

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Stanislav Kupin. On sum rules of special form for Jacobi matrices. Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 611-614. doi : 10.1016/S1631-073X(03)00132-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00132-8/

Bibliographie
Cité par

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David Damanik; Rowan Killip; Barry Simon Perturbations of orthogonal polynomials with periodic recursion coefficients, Annals of Mathematics, Volume 171 (2010) no. 3, p. 1931 | DOI:10.4007/annals.2010.171.1931
S. Kupin Absolutely continuous spectrum of a Schrödinger operator on a tree, Journal of Mathematical Physics, Volume 49 (2008) no. 11 | DOI:10.1063/1.3005967
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Andrej Zlatoš Sum rules for Jacobi matrices and divergent Lieb–Thirring sums, Journal of Functional Analysis, Volume 225 (2005) no. 2, p. 371 | DOI:10.1016/j.jfa.2005.04.012

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