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The moment problem for the algebra of symmetric tensors

Banff International Research Station for Mathematical Innovation and Discovery

The univariate moment problem for the real polynomial ring is an old problem with origins tracing back to work of Stieltjes. The multivariate moment problem has been considered more recently. Even more recently, there has been considerable interest, for both pure theory and applications, in the infinite-variate moment problem, dealing with the moment problem in (possibly not finitely generated) real commutative unital algebras. In this talk we focus on a real (commutative unital) locally multiplicatively convex topological algebra and the representation of continuous linear functionals by Radon measures on its character space. We first prove a general representation theorem by measures supported on the Gelfand Spectrum of a real sub-multiplicative semi-normed real algebra. To this end, we exploit the Archimedean Positivstellensatz, which holds in its (Banach) completion, and then proceed to handle an arbitrary locally multiplicatively convex topology. We will illustrate the methods by examples. In particular, we apply our results to the symmetric tensor algebra of a locally convex real topological space. This talk is based on joint work with Ghasemi, Infusino and Marshall.

Mathematics; Operations research, mathematical programming; Algebraic geometry; Control/Optimization/Operation Research

video/mp4

Author affiliation: Universität Konstanz

2019-11-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72428

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/