Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points
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- by Franz Peherstorfer and Peter Yuditskii
- Proc. Amer. Math. Soc. 129 (2001), 3213-3220
- DOI: https://doi.org/10.1090/S0002-9939-01-06205-0
- Published electronically: May 21, 2001
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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.References
- J. S. Geronimo and K. M. Case, Scattering theory and polynomials orthogonal on the real line, Trans. Amer. Math. Soc. 258 (1980), no. 2, 467–494. MR 558185, DOI 10.1090/S0002-9947-1980-0558185-4
- Ya.L. Geronimus, Polynomials orthogonal on a circle and interval, Pergamon Press, New York, 1960.
- A.A. Gonchar, On convergence of Padé approximants for certain classes of meromorphic functions, Mat.Sb. 97 (1975), English translation: Math. USSR-Sb. 26.
- Paul G. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 18 (1979), no. 213, v+185. MR 519926, DOI 10.1090/memo/0213
- Paul Nevai, Research problems in orthogonal polynomials, Approximation theory VI, Vol. II (College Station, TX, 1989) Academic Press, Boston, MA, 1989, pp. 449–489. MR 1091045
- E. M. Nikishin, The discrete Sturm-Liouville operator and some problems of function theory, Trudy Sem. Petrovsk. 10 (1984), 3–77, 237 (Russian, with English summary). MR 778879
- E. M. Nikishin and V. N. Sorokin, Rational approximations and orthogonality, Translations of Mathematical Monographs, vol. 92, American Mathematical Society, Providence, RI, 1991. Translated from the Russian by Ralph P. Boas. MR 1130396, DOI 10.1090/mmono/092
- F. Peherstorfer and P Yuditskii, Asymptotic behavior of polynomials orthonormal on a homogeneous set, manuscript.
Bibliographic 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