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A family of Sobolev Orthogonal Polynomials on the Unit Ball

Yuan Xu
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Abstract

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.

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Yuan Xu. 2005-07-28. A family of Sobolev Orthogonal Polynomials on the Unit Ball. https://arxiv.org/abs/math/0507580

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