Weak classical orthogonal polynomials in two variables

Authors:
Lidia Fernández;Teresa E. Pérez;Miguel A. Piñar
Affiliations:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain;Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain;Departamento de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Year:
2005

Citing 4
Cited 2

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Abstract

Orthogonal polynomials in two variables constitute a very old subject in approximation theory. Usually they are studied as solutions of second-order partial differential equations. In this work, we study two-variable orthogonal polynomials associated with a moment functional satisfying the two-variable analogue of the Pearson differential equation. From this approach, we derive the extension of some of the usual characterizations of the classical orthogonal polynomials in one variable.