Journal of Applied Mathematics
Volume 2005 (2005), Issue 4, Pages 321-339

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

Copyright © 2005 V. A. Menegatto and A. C. Piantella. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.