Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier transformation of Sato's hyperfunctions   A new generalized function space in which all Gelfand-Shilov classes
$S^{\prime 0}_\alpha$ ($\alpha>1$) of analytic functionals are embedded is
introduced. This space of {\it ultrafunctionals} does not possess a natural
nontrivial topology and cannot be obtained via duality from any test function
space. A canonical isomorphism between the spaces of hyperfunctions and
ultrafunctionals on $R^k$ is constructed that extends the Fourier
transformation of Roumieu-type ultradistributions and is naturally interpreted
as the Fourier transformation of hyperfunctions. The notion of carrier cone
that replaces the notion of support of a generalized function for
ultrafunctionals is proposed. A Paley-Wiener-Schwartz-type theorem describing
the Laplace transformation of ultrafunctionals carried by proper convex closed
cones is obtained and the connection between the Laplace and Fourier
transformation is established.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con