International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 417-428
doi:10.1155/S0161171298000593

An embedding of Schwartz distributions in the algebra of asymptotic functions

Michael Oberguggenberger1 and Todor Todorov2

1Institut für Mathematik und Geometrie, Universität Innsbruck, Inssbruck A-6020, Austria
2Mathematics Department, California Polytechnic State University, San Luis Obispo 93407, California, USA

Received 28 October 1996; Revised 21 June 1997

Copyright © 1998 Michael Oberguggenberger and Todor Todorov. 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 present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper “asymptotic function,” similar to but different from J. F Colombeau's algebras of new generalized functions.