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.
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Title
The strong Hamburger moment problem and related direct and inverse spectral problems for block Jacobi-Laurent matrices
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},
MRNUMBER = {MR2743588},
URL = {http://mfat.imath.kiev.ua/article/?id=568},
}