New steps on Sobolev orthogonality in two variables |
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Authors: | Cleonice F. Bracciali,Miguel A. Piñ ar |
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Affiliation: | a DCCE, IBILCE, UNESP-Universidade Estadual Paulista, Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto, SP, Brazilb Dpto. de Matemática Aplicada and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain |
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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. |
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Keywords: | 42C05 33C50 |
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