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# The Nevanlinna-type formula for the matrix Hamburger moment problem

### Abstract

In this paper we obtain a Nevanlinna-type formula for the matrix Hamburger moment problem. We only assume that the problem is solvable and has more than one solution. We express the matrix coefficients of the corresponding linear fractional transformation in terms of the prescribed moments. Necessary and sufficient conditions for the determinacy of the moment problem in terms of the given moments are obtained.

### Article Information

 Title The Nevanlinna-type formula for the matrix Hamburger moment problem Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 4, 387-400 MathSciNet MR3058464 zbMATH 1289.44007 Copyright The Author(s) 2012 (CC BY-SA)

### Authors Information

S. M. Zagorodnyuk
School of Mathematics and Mechanics, Karazin Kharkiv National University, 4 Svobody sq., Kharkiv, 61077, Ukraine

### Citation Example

S. M. Zagorodnyuk, The Nevanlinna-type formula for the matrix Hamburger moment problem, Methods Funct. Anal. Topology 18 (2012), no. 4, 387-400.

### BibTex

@article {MFAT637,
AUTHOR = {Zagorodnyuk, S. M.},
TITLE = {The Nevanlinna-type formula for the matrix Hamburger moment problem},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {18},
YEAR = {2012},
NUMBER = {4},
PAGES = {387-400},
ISSN = {1029-3531},
MRNUMBER = {MR3058464},
ZBLNUMBER = {1289.44007},
URL = {http://mfat.imath.kiev.ua/article/?id=637},
}