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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points


Authors: Franz Peherstorfer and Peter Yuditskii
Journal: Proc. Amer. Math. Soc. 129 (2001), 3213-3220
MSC (2000): Primary 42C05, 30D50
Published electronically: May 21, 2001
MathSciNet review: 1844996
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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
Email: yuditskii@ilt.kharkov.ua, yuditski@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06205-0
PII: S 0002-9939(01)06205-0
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
Article copyright: © Copyright 2001 American Mathematical Society