Mathematical Physics
On sum rules of special form for Jacobi matrices
Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 611-614.

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).

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.

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DOI: 10.1016/S1631-073X(03)00132-8
Kupin, Stanislav 1

1 Department of Mathematics, Box 1917, Brown University, Providence, RI 02912, USA
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Kupin, Stanislav. 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. http://www.numdam.org/articles/10.1016/S1631-073X(03)00132-8/

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[4] R. Killip, B. Simon, Sum rules for Jacobi matrices and their applications to spectral theory, Ann. Math., to appear

[5] S. Kupin, On a spectral property of Jacobi matrices, Proc. Amer. Math. Soc, accepted

[6] A. Laptev, S. Naboko, O. Safronov, On new relations between spectral properties of Jacobi matrices and their coefficients, to appear

[7] Molchanov, S.; Novitskii, M.; Vainberg, B. First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator, Comm. Math. Phys., Volume 216 (2001), pp. 195-213

[8] B. Simon, A. Zlatos, Sum rules and the Szegö condition for orthogonal polynomials on the real line, submitted

[9] P. Yuditskii, private communication

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