## Abstract

Let ^{∞} = ×_{d=1} ^{∞} Given a closed set K ⊆ ^{∞} and s: S → where S denotes the set of tuples of nonnegative integers (n_{1},n_{2},..) with n_{d} > 0 for finitely many d, the K-moment problem on ^{∞} entails determining whether or not there exists a measure σ on ^{∞} so that supp σ ⊆ K and s(n) = ∫ ^{∞} x^{n} dσ (x) for all n ε S. We prove that σ exists if and only if a natural analogue of the Riesz-Haviland functional 葦_{s} is K-positive, i.e. if p(x) = σ_{0≤|n|≤ m} p_{n}x^{n} is any polynomial which is nonnegative for all x ∈ K, then 葦_{s}(p) = σ _{0≤|n|≤ m} p_{n}s(n) ≥ 0. We will also provide a sufficient condition for σ to be unique, an analogue of a celebrated theorem of K. Schmüdgen and an application to stochastic processes.

Original language | English |
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Article number | 1550024 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - 1 Dec 2015 |

## Keywords

- infinite dimensional analysis
- Moment problems

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics