A family of Sobolev Orthogonal Polynomials on the Unit Ball

2005/07/28 by Yuan Xu, Xu, Yuan
Mathematics · #42A38 #42B08 #42B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42A38 #msc:42B08 #msc:42B15

paper · pdf · doi:10.48550/arxiv.math/0507580

arxiv created 2005/07/28 · arxiv updated 2009/12/01

Abstract

A family of orthonormal polynomials on the unit ball B^d of \RR^d with respect to the inner product < f,g > = ∫_B^dΔ[(1-‖x‖²) f(x)] Δ[(1-‖x‖) g(x)] dx, where Δ is the Laplace operator, is constructed explicitly.

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• Sobolev orthogonal polynomials defined via gradient on the unit ball
• Weighted Sobolev orthogonal polynomials on the unit ball
• Sobolev orthogonal polynomials on the unit ball via outward normal derivatives
• Orthogonal polynomials and partial differential equations on the unit ball
• Sobolev orthogonal polynomials on product domains