On the solvability of the indefinite Hamburger moment problem

被引：0

作者：

Hu, Yongjian ^{[1
]}

Hao, Huifeng ^{[2
]}

Zhan, Xuzhou ^{[3
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Hebei Univ Engn, Dept Stat, Handan 056038, Peoples R China

[3] Beijing Normal Univ Zhuhai, Dept Math, Zhuhai 519087, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

关键词：

generalized Nevanlinna function; infinite Hamburger moment problem; Hankel matrix; characteristic degree; characteristic polynomial quadruple; quasidirect decomposition; McMillan degree; RATIONAL INTERPOLATION PROBLEM; HANKEL; BEZOUTIANS;

D O I：

10.3934/math.20231535

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：30023 / 30037

页数：15

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