Abstract
The strong Hamburger moment problem for a bi-infinite sequence { c n : n=0, ±1, ±2,…} can be described as follows: (1) Find conditions for the existence of a (positive) measure μ on (−∞, ∞) such that c n =∫ −∞ ∞ t n dμ( t) for all n. (2) When there is a solution, find conditions for uniqueness of the solution. (3) When there is more than one solution, describe the family of all solutions. In this paper a theory concerning question (3) is developed. In particular, an analog to the Nevanlinna parametrization describing the solutions of the classical Hamburger moment problem is given.
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