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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A relation between the coefficients in the recurrence formula and the spectral function for orthogonal polynomials


Author: Jeffrey S. Geronimo
Journal: Trans. Amer. Math. Soc. 260 (1980), 65-82
MSC: Primary 42C05
DOI: https://doi.org/10.1090/S0002-9947-1980-0570779-9
MathSciNet review: 570779
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Abstract: A relation is found between the rate of convergence of the coefficients in the recurrence formula for polynomials orthogonal on a segment of the real line and certain properties of the spectral function. The techniques of Banach algebras and scattering theory are used. The close connection between polynomials orthogonal on the unit circle and polynomials orthogonal on the real line is exploited.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0570779-9
Article copyright: © Copyright 1980 American Mathematical Society