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Solutions of the Strong Hamburger Moment Problem

✍ Scribed by Olav Njåstad

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
219 KB
Volume
197
Category
Article
ISSN
0022-247X

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✦ Synopsis

The strong Hamburger moment problem for a bi-infinite sequence c : n s 0, " n 4 Ž . 1, " 2, . . . can be described as follows: 1 Find conditions for the existence of a Ž . Ž . ϱ n Ž . Ž . positive measure on yϱ, ϱ such that c s H t d t for all n. 2 When n yϱ

Ž . 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 Ž . 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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