A family of Sobolev Orthogonal Polynomials on the Unit Ball

Details A family of Sobolev Orthogonal Polynomials on the Unit Ball A family of Sobolev Orthogonal Polynomials on the Unit Ball

2005-07-28

arxiv.org/abs/math/0507580v1

Mathematics

Classical Analysis and ODEs

Scientific paper

A family of orthonormal polynomials on the unit ball $B^d$ of $\RR^d$ with
respect to the inner product $$
< f,g >
= \int_{B^d}\Delta[(1-\|x\|^2) f(x)] \Delta[(1-\|x\|) g(x)] dx, $$ where
$\Delta$ is the Laplace operator, is constructed explicitly.

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