English

A family of Sobolev Orthogonal Polynomials on the Unit Ball

Classical Analysis and ODEs 2007-05-23 v1

Abstract

A family of orthonormal polynomials on the unit ball BdB^d of \RRd\RR^d with respect to the inner product <f,g>=BdΔ[(1x2)f(x)]Δ[(1x)g(x)]dx, < f,g > = \int_{B^d}\Delta[(1-\|x\|^2) f(x)] \Delta[(1-\|x\|) g(x)] dx, where Δ\Delta is the Laplace operator, is constructed explicitly.

Keywords

Cite

@article{arxiv.math/0507580,
  title  = {A family of Sobolev Orthogonal Polynomials on the Unit Ball},
  author = {Yuan Xu},
  journal= {arXiv preprint arXiv:math/0507580},
  year   = {2007}
}