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.
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.
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Sergey Denisov 1; Stanislas Kupin 2
@article{CRMATH_2004__339_4_241_0, author = {Sergey Denisov and Stanislas Kupin}, title = {Orthogonal polynomials and a generalized {Szeg\H{o}} condition}, journal = {Comptes Rendus. Math\'ematique}, pages = {241--244}, publisher = {Elsevier}, volume = {339}, number = {4}, year = {2004}, doi = {10.1016/j.crma.2004.06.004}, language = {en}, }
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/
[1] Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle, Linear Algebra Appl., Volume 362 (2003), pp. 29-56
[2] Necessary and sufficient conditions in the spectral theory of Jacobi matrices and Schrödinger operators, Int. Math. Res. Notices, Volume 22 (2004), pp. 1087-1097
[3] Orthogonal Polynomials, Consultants Bureau, New York, 1961
[4] Schur's algorithm, orthogonal polynomials, and convergence of Wall's continued fractions in , J. Approx. Theory, Volume 108 (2001) no. 2, pp. 161-248
[5] F. Nazarov, F. Peherstorfer, A. Volberg, P. Yuditskii, On generalized sum rules for Jacobi matrices, submitted for publication
[6] B. Simon, Orthogonal polynomials on the unit circle, Amer. Math. Soc. Colloq. Publ., in press
[7] Orthogonal Polynomials, American Mathematical Society, Providence, 1975
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