Generalized resolvents of symmetric operators
type: Item
instance of: scholarly article
title: Generalized resolvents of symmetric operators
zbMATH Open document ID: 1076.47002
DOI: 10.1023/A:1023282415426
published in: Mathematical Notes
publication date: 2004-11-15T00:00:00Z
review text: The Krein formula for generalized resolvents is one of the highlights of the theory of extensions of symmetric operators in Hilbert spaces. In the present paper, the authors give another more general version of such a formula for generalized \(U\)-resolvents of the isometric operator \(V\). Each boundary triple \(\Pi\) of \(\{V,V^{-1}\}\) generates the formula for generalized resolvents, and its parameters can be expressed in terms of the boundary operators. Now the Schur class of contractive operator-valued functions in the unit disk comes in. Note that there is a misprint in the title of the English version of the paper: ``isometric'' should be written rather than ``symmetric''.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B15
zbMATH DE Number: 2115584
zbMATH Keywords: Hilbert space
zbMATH Keywords: extension of an isometric operator
zbMATH Keywords: Krein formula
zbMATH Keywords: deficiency index
zbMATH Keywords: generalized resolvent
zbMATH Keywords: Schur class
author: M. M. Malamud
author: V. I. Mogilevskij
reviewed by: Leonid Golinskii
MaRDI profile type: Publication
full work available at URL: a:1023282415426
OpenAlex ID: W36219299
description: scientific article; zbMATH DE number 2115584