Frantisek Stampach: The Moment Problem

Abstract: We give a review on the classical moment problems of Hausdorff, Stieltjes and Hamburger. First, we recall main results concerning the existence and uniqueness of a solution of the moment problem. Further, we explain the relation between the moment problem, orthogonal polynomials and Jacobi matrices. At last, we discuss more closely the mathematically most interesting case when a solution of the moment problem exists but is not unique. No special prerequisites are needed (just standard package of mathematical analysis) but certain knowledge of operators and spectral theory is an advantage.