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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points
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by Franz Peherstorfer and Peter Yuditskii PDF
Proc. Amer. Math. Soc. 129 (2001), 3213-3220 Request permission

Abstract:

Let $\sigma$ be a positive measure whose support is an interval $E$ plus a denumerable set of mass points which accumulate at the boundary points of $E$ only. Under the assumptions that the mass points satisfy Blaschke’s condition and that the absolutely continuous part of $\sigma$ satisfies Szegö’s condition, asymptotics for the orthonormal polynomials on and off the support are given. So far asymptotics were only available if the set of mass points is finite.
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Additional Information
  • Franz Peherstorfer
  • Affiliation: Institute for Analysis and Computational Mathematics, Johannes Kepler University of Linz, A–4040 Linz, Austria
  • Email: Franz.Peherstorfer@jk.uni-linz.ac.at
  • Peter Yuditskii
  • Affiliation: Mathematical Division, Institute for Low Temperature Physics, Kharkov, Lenin’s pr. 47, 310164, Ukraine
  • Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 202230
  • Email: yuditskii@ilt.kharkov.ua, yuditski@math.msu.edu
  • Received by editor(s): February 15, 2000
  • Published electronically: May 21, 2001
  • Additional Notes: This work was supported by the Austrian Founds zur Förderung der wissenschaftlichen Forschung, project–number P12985–TEC
  • Communicated by: Juha M. Heinonen
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3213-3220
  • MSC (2000): Primary 42C05, 30D50
  • DOI: https://doi.org/10.1090/S0002-9939-01-06205-0
  • MathSciNet review: 1844996