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