A family of Sobolev orthogonal polynomials on the unit ball

Authors:
Yuan Xu
Affiliations:
Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA
Venue:
Journal of Approximation Theory
Year:
2006

Citing 1
Cited 2

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A spectral method for elliptic equations: the Neumann problem

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Full length article: Weighted Sobolev orthogonal polynomials on the unit ball

Journal of Approximation Theory

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Abstract

A family of orthonormal polynomials on the unit ball B^d of R^d with respect to the inner product=@!"B"^"d@D[(1-@?x@?^2)f(x)]@D[(1-@?x@?^2)g(x)]dx,where @D is the Laplace operator, is constructed explicitly.