New results in the classical moment problem

In the report we will discuss the connection between the classical power moment problem and relatively new branch of functional analysis - the theory of extrapolation of spaces and operators (shortly, extrapolation theory). Using the extrapolation theory, we describe symmetric function spaces which consist of random variables with determinate moment problem only. Thus, the moment problem is considered for the classes of random variables which form Banach spaces. Using this approach we get also some individual conditions for determinacy of moment problem. These conditions are close to Cramer condition in form, while by exactness they are close to Carleman condition. In addition, the following simple, but a new and unexpected result will be proved in the report: any random variable with all finite moments may be decomposed into a sum of two random variables with determinate moment problem.