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