## Arkiv för Matematik

• Ark. Mat.
• Volume 56, Number 2 (2018), 441-459.

### On the infinite-dimensional moment problem

#### 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 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 $A$.

#### Article information

Source
Ark. Mat., Volume 56, Number 2 (2018), 441-459.

Dates
Revised: 4 April 2018
First available in Project Euclid: 19 June 2019

https://projecteuclid.org/euclid.afm/1560968143

Digital Object Identifier
doi:10.4310/ARKIV.2018.v56.n2.a14

Mathematical Reviews number (MathSciNet)
MR3893784

Zentralblatt MATH identifier
07021448

#### Citation

Schmüdgen, Konrad. On the infinite-dimensional moment problem. Ark. Mat. 56 (2018), no. 2, 441--459. doi:10.4310/ARKIV.2018.v56.n2.a14. https://projecteuclid.org/euclid.afm/1560968143