Rank one perturbations at infinite coupling in Pontryagin spaces.
type: Item
instance of: scholarly article
title: Rank one perturbations at infinite coupling in Pontryagin spaces.
zbMATH Open document ID: 1068.47041
author: Yuri Shondin
author: A. Dijksma
author: Heinz Langer
published in: Journal of Functional Analysis
publication date: 2004-06-11T00:00:00Z
full work available at URL: 2004JFunctAnalDijksma.pdf
review text: The authors study Nevanlinna functions of class \({\mathcal N}^\infty_k\) which have \(k\) poles of nonpositive type in the upper half-plane and allow an irreducible representation \(N(z)= c(z)^m N_0(z)+ p(z)\), where \(c(z):= (z- z^*_0)\). The paper has five sections. The first gives an introduction to symmetric operators in Pontryagin spaces and Nevanlinna functions. Self-adjoint operators with cyclic elements in a Pontryagin space are studied in the second section. The main results of the paper are to be found in section 3, where the authors clarify the connections between some types of Nevanlinna functions, symmetric operators, self-adjoint operators and the corresponding Pontryagin/Hilbert spaces. Section 4 is devoted to the analytic and operator characterizations of the functions \(N(z)\) and \(\widehat N(z)\). Section 5 contains applications of this theory to Bessel operators, which motivates the entire study.
reviewed by: Trandafir Balan
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A06
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 2073663
zbMATH Keywords: Pontryagin space
zbMATH Keywords: Hilbert space
zbMATH Keywords: defect function
zbMATH Keywords: \(Q\)-function
zbMATH Keywords: generalized Nevanlinna function
zbMATH Keywords: infinite coupling
zbMATH Keywords: rank one perturbation
zbMATH Keywords: symmetric
zbMATH Keywords: operator
zbMATH Keywords: self-adjoint linear relation
zbMATH Keywords: extension theory
MaRDI profile type: Publication
OpenAlex ID: W2005829122
Wikidata QID: Q124629955
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DOI: 10.1016/J.JFA.2003.06.005
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description: scientific article; zbMATH DE number 2073663