Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moment problem for symmetric algebras of locally convex spaces   It is explained how a locally convex (lc) topology $\tau$ on a real vector
space $V$ extends to a locally multiplicatively convex (lmc) topology
$\overline{\tau}$ on the symmetric algebra $S(V)$. This allows the application
of the results on lmc topological algebras obtained by Ghasemi, Kuhlmann and
Marshall to obtain representations of $\overline{\tau}$-continuous linear
functionals $L: S(V)\rightarrow \mathbb{R}$ satisfying $L(\sum S(V)^{2d})
\subseteq [0,\infty)$ (more generally, $L(M) \subseteq [0,\infty)$ for some
$2d$-power module $M$ of $S(V)$) as integrals with respect to uniquely
determined Radon measures $\mu$ supported by special sorts of closed balls in
the dual space of $V$. The result is simultaneously more general and less
general than the corresponding result of Berezansky, Kondratiev and \v Sifrin.
It is more general because $V$ can be any lc topological space (not just a
separable nuclear space), the result holds for arbitrary $2d$-powers (not just
squares), and no assumptions of quasi-analyticity are required. It is less
general because it is necessary to assume that $L : S(V) \rightarrow
\mathbb{R}$ is $\overline{\tau}$-continuous (not just continuous on each
homogeneous part of $S(V)$).

33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th