Truncated Hamburger moment problem for an operator measure with compact support

被引：3

作者：

Arlinskii, Yury ^{[1
]}

机构：

[1] E Ukrainian Natl Univ, Dept Math, UA-91034 Lugansk, Ukraine

来源：

MATHEMATISCHE NACHRICHTEN | 2012年 / 285卷 / 14-15期

关键词：

N-simple operator; the Weyl function; the Schur transformation; the Schur parameters; the special block operator Jacobi matrix; moments; the Hankel matrix; the Krein shorted operator; PARAMETRIZATION; MATRICES; SCHUR;

D O I：

10.1002/mana.201200028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given bounded selfadjoint operators F-1 - I-n, F-2, ..., F2n+1 in a separable Hilbert space n, we consider the operator truncated Hamburger moment problem of finding a Herglotz-Nevanlinna operator-valued function M holomorphic in the neighborhood of infinity and having the form M(z) = -Sigma(2n + 1)(k = 1)z(-k)F(k) + o(z(-2n-1)), z -> infinity. Criteria of the solvability and uniqueness of the solution are established and a description of all solutions is obtained. Our approach is based on the Schur transformation, the Schur parameters, and the special block operator Jacobi matrices. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1677 / 1695

页数：19

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