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# The strong Hamburger moment problem and related direct and inverse spectral problems for block Jacobi-Laurent matrices

### Abstract

In this article we propose an approach to the strong Hamburger moment problem based on the theory of generalized eigenvectors expansion for a selfadjoint operator. Such an approach to another type of moment problems was given in our works earlier, but for strong Hamburger moment problem it is new. We get a sufficiently complete account of the theory of such a problem, including the spectral theory of block Jacobi-Laurent matrices.

Key words: Classical and strong moment problems, block three-diagonal matrix, eigenfunction expansion, generalized eigenvector.

### Article Information

 Title The strong Hamburger moment problem and related direct and inverse spectral problems for block Jacobi-Laurent matrices Source Methods Funct. Anal. Topology, Vol. 16 (2010), no. 3, 203-241 MathSciNet MR2743588 Copyright The Author(s) 2010 (CC BY-SA)

### Authors Information

Yurij M. Berezansky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Mykola E. Dudkin
National Technical University of Ukraine (KPI), 37 Peremogy Av., Kyiv, 03056, Ukraine

### Citation Example

Yurij M. Berezansky and Mykola E. Dudkin, The strong Hamburger moment problem and related direct and inverse spectral problems for block Jacobi-Laurent matrices, Methods Funct. Anal. Topology 16 (2010), no. 3, 203-241.

### BibTex

@article {MFAT568,
AUTHOR = {Berezansky, Yurij M. and Dudkin, Mykola E.},
TITLE = {The strong Hamburger moment problem and related direct and inverse spectral problems for block Jacobi-Laurent matrices},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {16},
YEAR = {2010},
NUMBER = {3},
PAGES = {203-241},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=568},
}