no. 5
Zero distributions via orthogonality
[Distributions asymptotiques de zéros et orthogonalité]
Baratchart, Laurent1 ; Küstner, Reinhold ; Totik, Vilmos
1 INRIA, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex (France), Université de Provence, LATP, CMI, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13 (France), University of Szeged, Bolyai Institute, Aradi v. tere 1, 6720 (Hongrie), University of South Florida, department of mathematics, Tampa FL 33620 (USA)
Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1455-1499.

On développe une nouvelle méthode pour établir la distribution asymptotique des zéros de divers polynômes orthogonaux sur un segment. Cette méthode exploite de manière directe les relations d'orthogonalité. Nous l'illustrons dans quatre cas : l'orthogonalité classique par rapport à une mesure positive, l'orthogonalité non-Hermitienne par rapport à une mesure complexe, et l'orthogonalité non-linéaire intervenant en approximation rationnelle, tout d'abord dans le cas d'une mesure positive, puis dans le cas non- Hermitien.

We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We illustrate the procedure in four cases: classical orthogonality, non-Hermitian orthogonality, orthogonality in rational approximation of Markov functions and its non- Hermitian variant.

DOI : 10.5802/aif.2130
Classification : 30C15, 30E10, 30E20, 31A15, 05E35, 42C05
Keywords: orthogonal polynomials, zero distribution, logarithmic potential, rational approximation
Mot clés : polynômes orthogonaux, distribution des zèros, potentiel logarithmique, approximation rationnelle

Baratchart, Laurent 1 ; Küstner, Reinhold  ; Totik, Vilmos 

1 INRIA, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex (France), Université de Provence, LATP, CMI, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13 (France), University of Szeged, Bolyai Institute, Aradi v. tere 1, 6720 (Hongrie), University of South Florida, department of mathematics, Tampa FL 33620 (USA) 
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Baratchart, Laurent; Küstner, Reinhold; Totik, Vilmos. Zero distributions via orthogonality. Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1455-1499. doi : 10.5802/aif.2130. https://aif.centre-mersenne.org/articles/10.5802/aif.2130/

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