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 | References | Similar Articles | Additional Information

Let be a positive measure whose support is an interval plus a denumerable set of mass points which accumulate at the boundary points of only. Under the assumptions that the mass points satisfy Blaschke's condition and that the absolutely continuous part of 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

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