On the infinite-dimensional moment problem

Konrad Schmüdgen

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arXiv · 1712.06360

On the infinite-dimensional moment problem

Konrad Schmüdgen

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Abstract

This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with respect to cylinder measures. Our main results provide such integral representations for $A_+$--positive linear functionals (generalized Haviland theorem) and for positive functionals fulfilling Carleman conditions. As an application we solve the moment problem for the symmetric algebra $S(V)$ of a real vector space $V$. As a byproduct we obtain a new approaches to the moment problem on $S(V)$ for a nuclear space $V$ and to the integral decomposition of continuous positive functionals on a barrelled nuclear topological algebra $A$.

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BibTeX RIS

Konrad Schmüdgen. 2017-12-18. On the infinite-dimensional moment problem. https://arxiv.org/abs/1712.06360

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