Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607270 | Journal of Approximation Theory | 2013 | 21 Pages |
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
Authors
Teresa E. Pérez, Miguel A. Piñar, Yuan Xu,