Orthogonal polynomials and a generalized Szegő condition

Sergey Denisov; Stanislas Kupin

doi:10.1016/j.crma.2004.06.004

Mathematical Analysis

Orthogonal polynomials and a generalized Szegő condition
[Polynômes orthogonaux et la condition de Szegő généralisée.]

Présenté par : Pierre-Louis Lions

Sergey Denisov ¹ ; Stanislas Kupin ²

¹ Department of Mathematics 253-37, Caltech, Pasadena, CA 91125, USA
² CMI, université de Provence, 39, rue Joliot Curie, 13453 Marseille cedex 13, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 241-244.

Résumé
Abstract

Les propriétés asymptotiques des polynômes orthogonaux de la classe de Szegő sont très bien étudiées. Nous obtenons les asymptotiques des polynômes orthogonaux appartenant à une classe considérablement plus large. Ensuite, nous appliquons cette information à l'étude du comportement spectral de ces derniers.

Asymptotical properties of orthogonal polynomials from the so-called Szegő class are very well-studied. We obtain asymptotics of orthogonal polynomials from a considerably larger class and we apply this information to the study of their spectral behavior.

Reçu le : 2004-04-05
Accepté le : 2004-06-01
Publié le : 2004-07-28

DOI : 10.1016/j.crma.2004.06.004

Affiliations des auteurs :

Sergey Denisov ¹ ; Stanislas Kupin ²

¹ Department of Mathematics 253-37, Caltech, Pasadena, CA 91125, USA
² CMI, université de Provence, 39, rue Joliot Curie, 13453 Marseille cedex 13, France

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     title = {Orthogonal polynomials and a generalized {Szeg\H{o}} condition},
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     pages = {241--244},
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     language = {en},
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Sergey Denisov; Stanislas Kupin. Orthogonal polynomials and a generalized Szegő condition. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 241-244. doi : 10.1016/j.crma.2004.06.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.004/

Bibliographie
Cité par

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L. Baratchart; S. Kupin; V. Lunot; M. Olivi Multipoint Schur algorithm and orthogonal rational functions. I: Convergence properties, Journal d'Analyse Mathématique, Volume 114 (2011), pp. 207-253 | DOI:10.1007/s11854-011-0016-9 | Zbl:1248.30015
Alexander Teplyaev A note on the theorems of M.G.Krein and L.A.Sakhnovich on continuous analogs of orthogonal polynomials on the circle, Journal of Functional Analysis, Volume 226 (2005) no. 2, pp. 257-280 | DOI:10.1016/j.jfa.2005.04.014 | Zbl:1082.34071

Cité par 2 documents. Sources : zbMATH

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