Abstract :
The strong Hamburger moment problem for a bi-infinite sequence cn: ns0,"
1,"2, . . .4can be described as follows: 1. Find conditions for the existence of a
positive.measure m on y`, `.such that cnsHy` `tndm 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. Q 1996 Academic Press, Inc.
