An axiomatic approach to non-linear theory of generalized functions
arXiv:1007.2223
Abstract
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of {\em Colombeau type} in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. The article is aimed at mathematicians and physicists who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.
I, Todor Todorov, withdrew this paper because the last two sections are missing. Please, see the paper "An axiomatic approach to non-linear theory of generalized functions and consistency of Laplace transform"