On the infinite-dimensional moment problem

Konrad Schmüdgen Universität Leipzig

Functional Analysis mathscidoc:1912.43025

Arkiv for Matematik, 56, (2), 441-459, 2019.12
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 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.
moment problem, cylinder measure, symmetric algebra, nuclear space, Carleman condition
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  title={On the infinite-dimensional moment problem},
  author={Konrad Schmüdgen},
  booktitle={Arkiv for Matematik},
Konrad Schmüdgen. On the infinite-dimensional moment problem. 2019. Vol. 56. In Arkiv for Matematik. pp.441-459. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204104710830497581.
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