Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On localization properties of Fourier transforms of hyperfunctions   In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized
function space $\mathcal U(R^k)$ which can be naturally interpreted as the
Fourier transform of the space of Sato's hyperfunctions on $R^k$. It was shown
that all Gelfand--Shilov spaces $S^{\prime 0}_\alpha(R^k)$ ($\alpha>1$) of
analytic functionals are canonically embedded in $\mathcal U(R^k)$. While the
usual definition of support of a generalized function is inapplicable to
elements of $S^{\prime 0}_\alpha(R^k)$ and $\mathcal U(R^k)$, their
localization properties can be consistently described using the concept of {\it
carrier cone} introduced by Soloviev [Lett. Math. Phys. 33 (1995) 49-59; Comm.
Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier
cones of elements of $S^{\prime 0}_\alpha(R^k)$ and $\mathcal U(R^k)$ is
studied. It is proved that an analytic functional $u\in S^{\prime
0}_\alpha(R^k)$ is carried by a cone $K\subset R^k$ if and only if its
canonical image in $\mathcal U(R^k)$ is carried by $K$.

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The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat