Positive polynomials and the moment problem for cylinders with compact cross-section

This paper concerns positive polynomials and the moment problem for certain non-compact cylinder-like closed semialgebraicsubsets . We extend Schweighoferʹs algorithm for SchmüdgenʹsPositivstellensatz in the compact case to this setting, for polynomials positive on the semialgebraic set with a certain extra boundedness condition. The idea is to use the Schweighofer algorithm to obtain a representation for each cross-section of the cylinder and then glue together the representations. The extra property is needed to ensure a uniform bound on the size of the representations on the cross sections. As a corollary, we show that the moment problem is solvable in this case.