中文

Sobolev orthogonal polynomials defined via gradient on the unit ball

经典分析与常微分方程 2007-05-23 v1

摘要

An explicit family of polynomials on the unit ball BdB^d of \RRd\RR^d is constructed, so that it is an orthonormal family with respect to the inner product <f,g>=ρBdf(x)g(x)dx+\CL(fg), < f,g > = \rho \int_{B^d}\nabla f(x)\cdot \nabla g(x) dx + \CL (fg), where ρ>0\rho >0, \nabla is the gradient, and \CL(fg)\CL(fg) is either the inner product on the sphere Sd1S^{d-1} or f(0)g(0)f(0)g(0).

关键词

引用

@article{arxiv.math/0612527,
  title  = {Sobolev orthogonal polynomials defined via gradient on the unit ball},
  author = {Yuan Xu},
  journal= {arXiv preprint arXiv:math/0612527},
  year   = {2007}
}

备注

12 pages