Open Access

# A description of all solutions of the matrix Hamburger moment problem in a general case

### Abstract

We describe all solutions of the matrix Hamburger moment problem in a general case (no conditions besides solvability are assumed). We use the fundamental results of A. V. Shtraus on the generalized resolvents of symmetric operators. All solutions of the truncated matrix Hamburger moment problem with an odd number of given moments are described in an "almost nondegenerate" case. Some conditions of solvability for the scalar truncated Hamburger moment problem with an even number of given moments are given.

### Article Information

 Title A description of all solutions of the matrix Hamburger moment problem in a general case Source Methods Funct. Anal. Topology, Vol. 16 (2010), no. 3, 271-288 MathSciNet MR2743592 Copyright The Author(s) 2010 (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, A description of all solutions of the matrix Hamburger moment problem in a general case, Methods Funct. Anal. Topology 16 (2010), no. 3, 271-288.

### BibTex

@article {MFAT535,
AUTHOR = {Zagorodnyuk, S. M.},
TITLE = {A description of all solutions of the matrix Hamburger moment problem in a general case},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {16},
YEAR = {2010},
NUMBER = {3},
PAGES = {271-288},
ISSN = {1029-3531},
MRNUMBER = {MR2743592},
URL = {http://mfat.imath.kiev.ua/article/?id=535},
}