Some generalizations of the classical moment problem

The article is devoted to two generalizations of the classical power moment problem, namely: 1) instead of representing the moment sequence by (lambda)n , a representation by polynomials Pn (lambda),(lambda)(element of) R1, connected with a Jacobi matrix, appears; 2) in the representation, instead of (lambda)n , the expression (lambda)(circled times)n figures, where (lambda) is a real generalized function (i.e., we investigate some infinite-dimensional moment problem).