Moment problem for algebras generated by a nuclear space

Abstract

We establish a criterion for the existence of a representing Radon measure for linear functionals defined on a unital commutative real algebra $A$, which we assume to be generated by a vector space $V$ endowed with a Hilbertian seminorm $q$. Such a general criterion provides representing measures with support contained in the space of characters of $A$ whose restrictions to $V$ are $q-$continuous. This allows us in turn to prove existence results for the case when $V$ is endowed with a nuclear topology. In particular, we apply our findings to the symmetric tensor algebra of a nuclear space.

arXiv comment30 pages

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Cited by in corpus (2)

• Infinite-dimensional moment-SOS hierarchy for nonlinear partial differential equations
• Solving moment and polynomial optimization problems on Sobolev spaces