New steps on Sobolev orthogonality in two variables

[摘要] 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.

[发布日期] 2010-12-15

[效力级别]  Proceedings Paper

[关键词] Orthogonal polynomials in two variables;Sobolev orthogonal polynomials;Classical orthogonal polynomials