On a generalization of the classical moment problem

Abstract

Let M ∗( R n ), R n, denote the set of all positive Borel measures on R n having moments of all orders. We study the following generalization of the classical moment problem: Given a multisequence { S α( S ij ()); α ϵ N n 0} of ( k, k) matrices with complex entries s ij ( α), when does there exist a nonnegative ( k, k) matrix Λ = ( λ ij ) of complex Borel measures λ ij on R n such that |γ ij | ϵ M ∗( R ij ) and s ij ( α) = ∫ x x dλ ij ( x) for all α ϵ N 0 n and i, j= 1,…, k?