THE STRONG HAMBURGER MOMENT PROBLEM AND RELATED DIRECT AND INVERSE SPECTRAL PROBLEMS FOR BLOCK JACOBI-LAURENT MATRICES

被引：0

作者：

Berezansky, Yurij M. ^{[1
]}

Dudkin, Mykola E. ^{[2
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, 3 Tereshchenkivska, UA-01601 Kiev, Ukraine

[2] Natl Tech Univ Ukraine KPI, UA-03056 Kiev, Ukraine

来源：

METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY | 2010年 / 16卷 / 03期

关键词：

Classical and strong moment problems; block three-diagonal matrix; eigenfunction expansion; generalized eigenvector;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we propose an approach to the strong Hamburger moment problem based on the theory of generalized eigenvectors expansion for a self-adjoint 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.

引用

页码：203 / 241

页数：39

共 44 条

[1] THE INNER STRUCTURE OF THE JACOBI-LAURENT MATRIX RELATED TO THE STRONG HAMBURGER MOMENT PROBLEM
Dudkin, Mykola E.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2013, 19 (02): : 97 - 107
[2] Laurent–Jacobi Matrices and the Strong Hamburger Moment Problem
Erik Hendriksen
Caspar Nijhuis
Acta Applicandae Mathematica, 2000, 61 : 119 - 132
[3] Laurent-Jacobi matrices and the strong hamburger moment problem
Hendriksen, E
Nijhuis, C
ACTA APPLICANDAE MATHEMATICAE, 2000, 61 (1-3) : 119 - 132
[4] THE COMPLEX MOMENT PROBLEM AND DIRECT AND INVERSE SPECTRAL PROBLEMS FOR THE BLOCK JACOBI TYPE BOUNDED NORMAL MATRICES
Berezansky, Yurij M.
Dudkin, Mykola E.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2006, 12 (01): : 1 - 31
[5] DIRECT AND INVERSE SPECTRAL PROBLEMS FOR BLOCK JACOBI TYPE BOUNDED SYMMETRIC MATRICES RELATED TO THE TWO DIMENSIONAL REAL MOMENT PROBLEM
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Kozak, Valentyna I.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2014, 20 (03): : 219 - 251
[6] THE COMPLEX MOMENT PROBLEM IN THE EXPONENTIAL FORM WITH DIRECT AND INVERSE SPECTRAL PROBLEMS FOR THE BLOCK JACOBI TYPE CORRESPONDENCE MATRICES
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METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2012, 18 (02): : 111 - 139
[7] ORTHOGONAL LAURENT POLYNOMIALS AND THE STRONG HAMBURGER MOMENT PROBLEM
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THRON, WJ
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[8] Nevanlinna matrices for the strong Hamburger moment problem
Njåstad, O
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2003, 33 (02) : 475 - 488
[9] SOLUTION OF THE STRONG HAMBURGER MOMENT PROBLEM BY LAURENT CONTINUED FRACTIONS
NJASTAD, O
APPLIED NUMERICAL MATHEMATICS, 1988, 4 (2-4) : 351 - 360
[10] Inverse problem for dynamical system associated with Jacobi matrices and classical moment problems
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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 487 (01)

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