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arxiv: math/0507580 · v1 · submitted 2005-07-28 · 🧮 math.CA

A family of Sobolev Orthogonal Polynomials on the Unit Ball

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keywords deltaballfamilypolynomialsunitconstructedexplicitlyinner
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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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