Orthogonal expansions for generalized Gegenbauer weight function on the unit ball

2015/02/09 by Xu, Yuan
#33C45 #33C50 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.02379

Abstract

Orthogonal polynomials and expansions are studied for the weight function h_κ²(x) ‖x‖^2ν (1-‖x‖²)^μ-1/2 on the unit ball of ℝ^d, where h_κ is a reflection invariant function, and for related weight function on the simplex of ℝ^d. A concise formula for the reproducing kernels of orthogonal subspaces is derived and used to study summability of the Fourier orthogonal expansions.

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