Journal of Applied Mathematics 
Volume 2005 (2005), Issue 4, Pages 321-339
doi:10.1155/JAM.2005.321

Approximation on the sphere by weighted Fourier expansions

V. A. Menegatto and A. C. Piantella

 Departamento de Matemática, Instituto de Ciências Matemáticas de Computação, Universidade de São Paulo - São Carlos, Caixa Postal 668, São Carlos 13560-970, SP, Brazil
Received 2 March 2005; Revised 12 September 2005

Abstract

The main theme of this paper is the approximation on the sphere by weighted sums of spherical harmonics. We give necessary and sufficient conditions on the weights for convergence in both the continuous and the LP cases. Approximation by spherical convolution is a particular and important case that fits into our setting.