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Mass points of measures on the unit circle and reflection coefficients
Author(s):
Leonid
Golinskii
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1771-1776.
MSC (2000):
Primary 42C05
Posted:
October 1, 2002
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Abstract:
Measures on the unit circle and orthogonal polynomials are completely determined by their reflection coefficients through the Szego recurrences. We find the conditions on the reflection coefficients which provide the lack of a mass point at  . We show that the result is sharp in a sense.
References:
-
- [1]
- L. Ya. (aka Ya. L.) Geronimus, Orthogonal Polynomials: Estimates, asymptotic formulas, and series of polynomials orthogonal on the unit circle and on an interval, Consultants Bureau, New York, 1961. MR 24:A3469
- [2]
- Ya. L. Geronimus, Polynomials orthogonal on a circle and their applications, Series and Approximations, Amer. Math. Soc. Transl. (1), vol. 3, Providence, Rhode Island, 1962, pp. 1-78.
- [3]
- P. Nevai, Orthogonal polynomials, measures and recurrences on the unit circle, Trans. Amer. Math. Soc. 300 (1987), 175-189. MR 88d:42041
- [4]
- J. A. Shohat and J. D. Tamarkin, The Problem of Moments, Math. Surveys, vol. 1, Amer. Math. Soc., Providence, Rhode Island, 1970. MR 5:5c
- [5]
- G. Szego, Orthogonal Polynomials, Fourth edition, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, Rhode Island, 1975. MR 51:8724
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Additional Information:
Leonid
Golinskii
Affiliation:
Mathematics Division, Institute for Low Temperature Physics and Engineering, 47 Lenin Avenue, Kharkov 61103, Ukraine
Email:
golinskii@ilt.kharkov.ua
DOI:
10.1090/S0002-9939-02-06706-0
PII:
S 0002-9939(02)06706-0
Keywords:
Measures on the unit circle,
orthogonal polynomials,
Szeg\H o recurrence relations
Received by editor(s):
December 13, 2001
Received by editor(s) in revised form:
January 14, 2002
Posted:
October 1, 2002
Additional Notes:
This material is based on work supported by the INTAS Grant 2000-272
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2002,
American Mathematical Society
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