SOLUTIONS OF THE STRONG HAMBURGER MOMENT PROBLEM

The strong Hamburger moment problem for a bi-infinite sequence {c(n) : n = 0, +/- 1, +/- 2,...} can be described as follows: (1) Find condit ions for the existence of a (positive) measure mu on (-infinity,infini ty) such that c(n) = integral(-infinity)(infinity)t(n) d mu(t) for all n. (2) When there is a solution, find conditions for uniqueness of th e solution. (3) When there is more than one solution, describe the fam ily of all solutions. In this paper a theory concerning question (3) i s developed. In particular, an analog to the Nevanlinna parametrizatio n describing the solutions of the classical Hamburger moment problem i s given. (C) 1996 Academic Press, Inc.