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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- 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: email@example.com, firstname.lastname@example.org
- 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