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Orthogonal Polynomials and Rational Modifications of Measures

Published online by Cambridge University Press:  20 November 2018

E. Godoy  and
F. Marcellan
E. Godoy
Affiliation:
Universidadde Vigo Departamento de Matematica Aplicada Escuela Tecnica Superior de Ingenieros Industriales Apartado de Correos, No. 62 36280-VIGO Spain
F. Marcellan
Affiliation:
Universidad Carlos III de Madrid Escuela Politecnica Superior Avdadel Mediterraneo, s/n 28913 LEGANES Madrid Spain
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Abstract

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Given a finite positive measure on the Borel subsets of the complex plane with compact support containing infinitely many points, we deduce some formulas for the sequence of monic orthogonal polynomials associated to a rational modification of the measure. These expressions depend on so called functions of the second kind. Some examples for particular Jordan curves are given

Keywords

42C05Orthogonal polynomialsmeasuresrational modifications
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 930 - 943
Copyright
Copyright © Canadian Mathematical Society 1993

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