New steps on Sobolev orthogonality in two variables

Authors:
Cleonice F. Bracciali;Antonia M. Delgado;Lidia Fernández;Teresa E. Pérez;Miguel A. Piñar
Affiliations:
DCCE, IBILCE, UNESP-Universidade Estadual Paulista, Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto, SP, Brazil;Dpto. de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain;Dpto. de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain;Dpto. de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain;Dpto. 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
Year:
2010

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Abstract

Sobolev orthogonal polynomials in two variables are defined via inner products involving gradients. Such a kind of inner product appears in connection with several physical and technical problems. Matrix second-order partial differential equations satisfied by Sobolev orthogonal polynomials are studied. In particular, we explore the connection between the coefficients of the second-order partial differential operator and the moment functionals defining the Sobolev inner product. Finally, some old and new examples are given.