Zero distributions via orthogonality

Laurent Baratchart[1]; Reinhold Küstner; Vilmos Totik

  • [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 (2005)

  • Volume: 55, Issue: 5, page 1455-1499
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Baratchart, Laurent, Küstner, Reinhold, and Totik, Vilmos. "Zero distributions via orthogonality." Annales de l’institut Fourier 55.5 (2005): 1455-1499. <http://eudml.org/doc/116223>.

@article{Baratchart2005,
abstract = {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.},
affiliation = {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)},
author = {Baratchart, Laurent, Küstner, Reinhold, Totik, Vilmos},
journal = {Annales de l’institut Fourier},
keywords = {orthogonal polynomials; zero distribution; logarithmic potential; rational approximation},
language = {eng},
number = {5},
pages = {1455-1499},
publisher = {Association des Annales de l'Institut Fourier},
title = {Zero distributions via orthogonality},
url = {http://eudml.org/doc/116223},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Baratchart, Laurent
AU - Küstner, Reinhold
AU - Totik, Vilmos
TI - Zero distributions via orthogonality
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 5
SP - 1455
EP - 1499
AB - 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.
LA - eng
KW - orthogonal polynomials; zero distribution; logarithmic potential; rational approximation
UR - http://eudml.org/doc/116223
ER -

References

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