International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 625-636
Regularization of distributions
Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica
Received 12 November 1996
Copyright © 1998 Ricardo Estrada. 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.
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.