Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two classes of generalized functions used in nonlocal field theory   We elucidate the relation between the two ways of formulating causality in
nonlocal quantum field theory: using analytic test functions belonging to the
space $S^0$ (which is the Fourier transform of the Schwartz space $\mathcal D$)
and using test functions in the Gelfand-Shilov spaces $S^0_\alpha$. We prove
that every functional defined on $S^0$ has the same carrier cones as its
restrictions to the smaller spaces $S^0_\alpha$. As an application of this
result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular
generalized functions of tempered growth and obtain the corresponding extension
of Vladimirov's algebra of functions holomorphic on a tubular domain.

1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th