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.

Full Text

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},
  MRNUMBER = {MR2743588},
       URL = {http://mfat.imath.kiev.ua/article/?id=568},
}