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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 4, Pages 625-636
http://dx.doi.org/10.1155/S016117129800088X

Regularization of distributions

Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica

Received 12 November 1996

Copyright © 1998 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

We give a simple necessary and sufficient condition for the existence of distributional regularizations. Our results apply to functions and distributions defined in the complement of a point, in one or several variables. We also consider functions defined in the complement of a hypersurface. We apply these results to the existence of distributional boundary values of harmonic and analytic functions.