Moment problem for symmetric algebras of locally convex spaces
| Autor: | Murray Marshall, Salma Kuhlmann, Maria Infusino, Mehdi Ghasemi |
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| Rok vydání: | 2015 |
| Předmět: |
Symmetric algebra
Algebra and Number Theory Dual space 44A60 14P99 010102 general mathematics Nuclear space Topological space 16. Peace & justice Space (mathematics) 01 natural sciences Separable space Functional Analysis (math.FA) Moment problem Combinatorics Mathematics - Functional Analysis Mathematics - Algebraic Geometry Locally convex topological vector space 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Algebraic Geometry (math.AG) Analysis Mathematics |
| DOI: | 10.48550/arxiv.1507.06781 |
| Popis: | 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 $S(V)$). Comment: 19 pages, revised according to referee's comments, updated references, to appear in Integral Equations and Operator Theory |
| Databáze: | OpenAIRE |
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