New steps on Sobolev orthogonality in two variables - Bracciali, Cleonice Fátima [UNESP]; Delgado, Antonia M.; Fernandez, Lidia; Perez, Teresa E.; Pinar, Miguel A. (Elsevier B.V., 2010)
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. (C) 2010 Elsevier B.V. All rights reserved.
Keywords: Orthogonal polynomials in two variables; Sobolev orthogonal polynomials; Classical orthogonal polynomials