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Perturbation of Orthogonal Polynomials on an Arc of the Unit Circle, II

✍ Scribed by Leonid Golinskii; Paul Nevai; Ferenc Pintér; Walter Van Assche

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
222 KB
Volume
96
Category
Article
ISSN
0021-9045

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✦ Synopsis

Orthogonal polynomials on the unit circle are fully determined by their reflection coefficients through the Szego recurrences. Assuming that the reflection coefficients converge to a complex number a with 0< |a| <1, or, in addition, they form a sequence of bounded variation, we analyze the orthogonal polynomials by comparing them with orthogonal polynomials with constant reflection coefficients which were studied earlier by Ya. L. Geronimus and N. I. Akhiezer. In particular, we present asymptotic relations under certain assumptions on the rate of convergence of the

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