A family of Sobolev orthogonal polynomials on the unit ball

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

Citing 1
Cited 2

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Sobolev orthogonal polynomials defined via gradient on the unit ball

Journal of Approximation Theory
New steps on Sobolev orthogonality in two variables

Journal of Computational and Applied Mathematics

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Abstract

A family of orthonormal polynomials on the unit ball Bd of Rd with respect to the inner product (f,g) = ∫Bd Δ[(1-||x||2)f(x)]Δ[(1-||x||2)g(x)]dx, where Δ is the Laplace operator, is constructed explicitly.