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On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures

Published online by Cambridge University Press:  20 November 2018

Antonio J. Duran
Antonio J. Duran*
Affiliation:
Departamento de Análisis Matemático Universidad de Sevilla Apdo.1160 41080-Sevilla, Spain
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Abstract

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In this paper, we prove that any sequence of polynomials (pn)n for which dgr(pn) = n which satisfies a (2N + l)-term recurrence relation is orthogonal with respect to a positive definite N × N matrix of measures. We use that result to prove asymptotic properties of the kernel polynomials associated to a positive measure or a positive definite matrix of measures. Finally, some examples are given.

Keywords

42C0515A57orthogonal polynomialsrecurrence relationpositive definite matrices
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 1 , 01 February 1995 , pp. 88 - 112
Copyright
Copyright © Canadian Mathematical Society 1995

References

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