Comptes Rendus
no. 7
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 Kupin1
1 Department of Mathematics, Box 1917, Brown University, Providence, RI 02912, USA
Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 611-614.

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

[1] K. Case Orthogonal polynomials from the viewpoint of scattering theory, J. Math. Phys., Volume 15 (1974), pp. 2166-2174

[2] K. Case Orthogonal polynomials, II, J. Math. Phys., Volume 16 (1975), pp. 1435-1440

[3] D. Hundertmark; B. Simon Lieb–Thirring inequalities for Jacobi matrices, J. Approx. Theory, Volume 118 (2002), pp. 106-130

[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] S. Molchanov; M. Novitskii; B. Vainberg 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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