Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the characterization of Gelfand-Shilov-Roumieu spaces   Generalized $\mathbf{m}$-Gelfand-Shilov-Roumieu vector spaces
$\mathcal{S}_{\mathbf{m}}(\mathbf{X})$ are introduced. Here $\mathbf{m} =
(m^{(1)},...,m^{(n)})$, $\mathbf{X}=(X_{1},...,X_{n})$ and
$m^{(1)},...,m^{(n)}$ are sequences of positive real numbers and
$X_{1},...,X_{n}$ are operators in a Hilbert space. Conditions are given on the
sequences $m^{(1)},...,m^{(n)}$ and on the operators $X_{1},...,X_{n}$ so that
the equality $S_{\mathbf{m}}(\mathbf{X}) = S_{m^{(1)}}(X_{1})\cap ...
\cap{S}_{m^{(n)}}(X_{n})$ is valid. As a corollary we obtain a new proof of a
characterization theorem for classical Gelfand-Shilov spaces.

31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph