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Asymptotic behaviour of orthogonal polynomials relative to measures with mass points

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  26 February 2010

José J. Guadalupe ,
M. Pérez ,
Francisco J. Ruiz  and
Juan L. Varona
José J. Guadalupe
Affiliation:
Dpto. de Matemáticas, Universidad de Zaragoza50009 Zaragoza, Spain.
M. Pérez
Affiliation:
Dpto. de Matemáticas, Universidad de Zaragoza50009 Zaragoza, Spain.
Francisco J. Ruiz
Affiliation:
Dpto. de Matemáticas, Universidad de Zaragoza50009 Zaragoza, Spain.
Juan L. Varona
Affiliation:
Dpto. de Matemática Aplicada, Colegio Universitario de La Rioja26001 LogroñoSpain.
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Abstract

General expressions are found for the orthonormal polynomials and the kernels relative to measures on the real line of the form μ + Mδc, in terms of those of the measures dμ and (x − c)2dμ. In particular, these relations allow us to show that Nevai's class M(0, 1) is closed under adding a mass point, as well as obtain several bounds for the polynomials and kernels relative to a generalized Jacobi weight with a finite number of mass points.

MSC classification

Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 331 - 344
Copyright
Copyright © University College London 1993

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