Wednesday, January 16, 2019 — 3:30 PM EST

Tobias Fritz, Perimeter Institute

"A separation theorem for order unit modules, with applications to random walks and the Laplace transform"

I will introduce order unit modules over ordered commutative R-algebras. I will then state the moment problem for order unit modules, and present a very general solution. This solution involves a certain locally convex topology which specializes to the topology of compact convergence in the case of a polynomial ring. Dualizing this solution of the moment problem gives a separation theorem which specializes to the Hahn-Banach theorem for order unit spaces in the case where the algebra is R, and to a Positivstellensatz in the case where the module coincides with the algebra. In the case of a suitable algebra of measures under convolution, these results also specialize to characterizations of Laplace transforms and to a new theorem on the asymptotic comparison of random walks.

MC 5417

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