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Orthogonal Polynomials and Quadratic Transformations

By (Spain)) Madrid 28911 Leganes Univ. Carlos III C. Butarque 15 Escuela Politecnica Superior F. (Dep. de Matematicas Marcellan and 3000 Coimbra (Portugal)) Univ. de Coimbra J. (Dep. de Matematica Petronilho

Abstract

Starting from a sequence #left brace#P_n#right brace#n#>=#o of monic polynomials orthogonal with respect to a linear functional #mu#, we find a linear functional#nu# such that Q_n n#>=#o, with either Q_2_n(#chi# P_n(T(#chi#)) or Q_2_n+1(#chi#) (#chi# - #alpha#)P_n(T(#chi#) where T is a monic quadratic polynomial and #alpha# a complex number, is a sequence of monic orthogonal polynomials with respect to #nu#. In particular, we discuss the case when #mu# and #nu# are both positive definite linear functionals. Thus, we obtain a solution for an inverse problem which is a converse, for quadratic mappings, of one analyzed by J.Geronimo and W.Van Assche ("Orthogonal Polynomials on Several Intervals via a Polynomial Mapping, Trans. Amer. Math. Soc., 308 (2),1988,559-581)Available from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga

Topics: 12A - Pure mathematics
Publisher: Coimbra : Univ. de Coimbra
Year: 1996
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Provided by: OpenGrey Repository
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