Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An axiomatic approach to the non-linear theory of generalized functions
  and consistency of Laplace transforms   We offer an axiomatic definition of a differential algebra of generalized
functions over an algebraically closed non-Archimedean field. This algebra is
of 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. Next, we identify an inconsistency in the
conventional Laplace transform theory. As an application we offer a free of
contradictions alternative in the framework of our algebra of generalized
functions. The article is aimed at mathematicians, physicists and engineers 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.

29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph