## Weighted approximation on the unit sphere

- Sept. 9, 2004
- 3:30 p.m.
- LeConte 312

## Abstract

For a family of weighted functions invariant under a finite reflection group, the direct and inverse theorems are established for the best approximation in the weighted L^p space on the unit sphere of R^d. The theorems are stated using a modulus of smoothness of higher order, defined through a generalized spherical means, which is shown to be equivalent to a K-functional, defined using the power of the spherical h-Laplacian.