The two-dimensional moment problem in a strip

Abstract

In this paper we study the two-dimensional moment problem in a strip $\Pi(R) = \{ (x_1,x_2)\in \mathbb{R}^2:\ |x_2| \leq R \}$, $R>0$. We obtained an analytic parametrization of all solutions of this moment problem. Usually the problem is reduced to an extension problem for a pair of commuting symmetric operators but we have no possibility to construct such extensions in larger spaces in a direct way. It turns out that we can find solutions without knowing the corresponding extensions in larger spaces. We used the fundamental results of Shtraus on generalized resolvents and some results from the measure theory.