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

 

Mass points of measures on the unit circle and reflection coefficients


Author: Leonid Golinskii
Journal: Proc. Amer. Math. Soc. 131 (2003), 1771-1776
MSC (2000): Primary 42C05
Published electronically: October 1, 2002
MathSciNet review: 1955264
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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 $\zeta =1$. We show that the result is sharp in a sense.


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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: http://dx.doi.org/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
Published electronically: October 1, 2002
Additional Notes: This material is based on work supported by the INTAS Grant 2000-272
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society