Solutions of the Strong Hamburger Moment Problem

Abstract

ÄThe 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 yϱŽ . 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. ᮊ

Spectral sets of periodic matrices related to the strong moment problem

“…They are related to the strong moment problem, see e.g. [19] and [6], and we take a risk to introduce an abbreviation and call them SMP matrices.…”

Analytic functions associated with strong Hamburger moment problems

“…This is the Riesz criterion for the strong Hamburger moment problem (see [12]). This is the Riesz criterion for the strong Hamburger moment problem (see [12]).…”

On the strong matrix Hamburger moment problem

“…In particular, conditions for the solvability of this problem were established in [2]. Solutions of the strong scalar Hamburger moment problem under certain regularity conditions were described in 1996 in [3] (see also [4]). …”