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
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.
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.