The extension theory of Hermitian operators and the moment problem
type: Item
instance of: scholarly article
title: The extension theory of Hermitian operators and the moment problem
zbMATH Open document ID: 0848.47004
DOI: 10.1007/BF02367240
author: V. A. Derkach
author: M. M. Malamud
published in: Journal of Mathematical Sciences (New York)
publication date: 1996-04-23T00:00:00Z
review text: This paper deals with the extension theory of a nondensely defined Hermitian operator in a Hilbert space. Generalized resolvents, preresolvent and resolvent matrices of such an operator are investigated. Necessary and sufficient conditions for a holomorphic operator-valued function to be a preresolvent or resolvent matrix of a Hermitian operator are found. A criterion for an \(R\)-function to be the Weyl function of a Hermitian operator is given. Applications to describe solutions of the truncated Hamburger, Stieltjes and Hausdorff moment problems are given. The results of this paper were partially announced in previous papers of the authors [Dokl. Akad. Nauk Ukr., Ser. A 11, 34-39 (1991); Dokl. Akad Nauk 323, No. 5, 816-822 (1992; Zbl 0820.47007); Dokl. Akad. Nauk 326, No. 1, 12-18 (1992)].
reviewed by: Jingbo Wu
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 859204
zbMATH Keywords: generalized resolvents
zbMATH Keywords: extension theory
zbMATH Keywords: nondensely defined Hermitian operator
zbMATH Keywords: preresolvent
zbMATH Keywords: resolvent matrices
zbMATH Keywords: holomorphic operator-valued function
zbMATH Keywords: resolvent matrix of a Hermitian operator
zbMATH Keywords: \(R\)-function
zbMATH Keywords: Weyl function
zbMATH Keywords: truncated Hamburger, Stieltjes and Hausdorff moment problems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 859204