q-coherent pairs and q-orthogonal polynomials

Authors:
I. Area;E. Godoy;F. Marcellán
Affiliations:
Departamento de Matemática Aplicada, E.T.S.I. Industriales y Minas, Universidad de Vigo, Campus Lagoas-Marcosende, 36200 Vigo, Spain;Departamento de Matemática Aplicada, E.T.S.I. Industriales y Minas, Universidad de Vigo, Campus Lagoas-Marcosende, 36200 Vigo, Spain;Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, c/Butarque 15, 28911 Leganés (Madrid), Spain
Venue:
Applied Mathematics and Computation - Orthogonal systems and applications
Year:
2002

Citing 5
Cited 2

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Inner products involving q-differences: the little qLaguerre-Sobolev polynomials

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The semiclassical Sobolev orthogonal polynomials: A general approach

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(1, 1)-q-coherent pairs

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Abstract

In this paper we introduce the concept of q-coherent pair of linear functionals. We prove that if (u0, u1) is a q-coherent pair of linear functionals, then at least one of them has to be a q-classical linear functional. Moreover, we present the classification of all q- coherent pairs of positive-definite linear functionals when u0 or u1 is either the little q- Jacobi linear functional or the little q-Laguerre/Wall linear functional. Finally, by using limit processes, we recover the classification of coherent pairs of linear functionals stated by Meijer.