On the solvability of the indefinite Hamburger moment problem

Abstract

In this paper, we present a new approach for the solvability of the indefinite Hamburger moment problem in the class of generalized Nevanlinna functions with a given negative index, which is more algebraic and completely different from the existing method [8] based on the step-by-step Schur algorithm. As a by-product of this approach, we simultaneously obtain a concrete rational solution of such an indefinite Hamburger moment problem when the solvability conditions are met. The basic strategy focuses on the structural characteristics of the Hankel matrix and the relation among the Hankel, Loewner, Bezout and some other structured matrices.

Keywords

• generalized nevanlinna function
• infinite hamburger moment problem
• hankel matrix
• characteristic degree
• characteristic polynomial quadruple
• quasidirect decomposition
• mcmillan degree