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Journal of Applied Mathematics
Volume 2005, Issue 2, Pages 93-115
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.