Journal of Applied Mathematics
Volume 2005 (2005), Issue 2, Pages 93-115
doi:10.1155/JAM.2005.93
Approximate solutions of equations defined by complex spherical multiplier operators
Instituto de Ciências Exatas, Universidade Federal de Itajubá, Caixa Postal 50, Itajubá 37500-903, MG, Brazil
Received 20 January 2004; Revised 9 December 2004
Copyright © 2005 C. P. Oliveira. 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
This paper studies, in a partial but concise manner, approximate solutions of equations defined by complex spherical multiplier operators. The approximations are from native spaces embedded in Sobolev-type spaces and derived from the use of positive definite functions to perform spherical interpolation.