An axiomatic approach to non-linear theory of generalized functions

Details An axiomatic approach to non-linear theory of generalized functions An axiomatic approach to non-linear theory of generalized functions

2010-07-13

arxiv.org/abs/1007.2223v3

Mathematics

Functional Analysis

I, Todor Todorov, withdrew this paper because the last two sections are missing. Please, see the paper "An axiomatic approach

Scientific paper

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.

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