Article ID Journal Published Year Pages File Type
4607270 Journal of Approximation Theory 2013 21 Pages PDF
Abstract

For the weight function Wμ(x)=(1−|x|2)μWμ(x)=(1−|x|2)μ, μ>−1μ>−1, λ>0λ>0 and bμbμ a normalizing constant, a family of mutually orthogonal polynomials on the unit ball with respect to the inner product 〈f,g〉=bμ[∫Bdf(x)g(x)Wμ(x)dx+λ∫Bd∇f(x)⋅∇g(x)Wμ(x)dx] are constructed in terms of spherical harmonics and a sequence of Sobolev orthogonal polynomials of one variable. The latter ones, hence, the orthogonal polynomials with respect to 〈⋅,⋅〉〈⋅,⋅〉, can be generated through a recursive formula.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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