An analytic characterization of the eigenvalues of self-adjoint extensions
type: Item
instance of: scholarly article
title: An analytic characterization of the eigenvalues of self-adjoint extensions
zbMATH Open document ID: 1114.47037
author: Jussi Behrndt
author: Annemarie Luger
published in: Journal of Functional Analysis
publication date: 2007-01-16T00:00:00Z
review text: In this paper, the analytic characterization of the eigenvalues of self-adjoint extensions is generalized. Also, a class of boundary value problems with boundary conditions depending on the spectral parameter is analyzed, which is closely connected with the self-adjoint extensions of a symmetric operator. The paper recalls the necessary definitions and basic properties of self-adjoint operators, introduces the concept of generalized values of local generalized Nevanlinna functions, and studies the behaviour of these functions at such points. The main results are contained in the fourth section of the paper; in the last section, as an application of the results, a class of abstract eigenvalue dependent boundary value problems is investigated. Also, as an example, a singular Sturm-Liouville operator with the signum function as indefinite weight in a Krein space is studied.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 5116377
zbMATH Keywords: Krein space
zbMATH Keywords: self-adjoint extension
zbMATH Keywords: Krein-Naimark formula
zbMATH Keywords: (locally) definitizable operator
zbMATH Keywords: (locally) generalized Nevanlinna function
zbMATH Keywords: generalized pole and zero
zbMATH Keywords: boundary value problem
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.09.011
OpenAlex ID: W2145277513
cites work: On locally definitizable matrix functions
cites work: Spectral points of type \(\pi_{+}\) and \(\pi_{-}\) of self-adjoint operators in Krein spaces
cites work: A class of nonlinear elliptic boundary value problems
cites work: On compact perturbations of locally definitizable selfadjoint relations in Krein spaces
cites work: Boundary value problems with local generalized Nevanlinna functions in the boundary condition
cites work: Sturm--Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions
cites work: Q3592913
cites work: Sturm–Liouville problems with eigenparameter dependent boundary conditions
cites work: Q3791731
cites work: The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces
cites work: On Weyl function and generalized resolvents of a Hermitian operator in a Krein space
cites work: On generalized resolvents of Hermitian relations in Krein spaces
cites work: Generalized resolvents and the boundary value problems for Hermitian operators with gaps
cites work: The extension theory of Hermitian operators and the moment problem
cites work: Generalized resolvents of symmetric operators and admissibility
cites work: Operator models associated with singular perturbations
cites work: Q4863701
cites work: Q3027731
cites work: Q4661915
cites work: Q3762877
cites work: Q4204839
cites work: Eigenvalues and Pole Functions of Hamiltonian Systems with Eigenvalue Depending Boundary Conditions
cites work: Q3999244
cites work: Q3411033
cites work: Q4218793
cites work: Q4743338
cites work: Q5443329
cites work: Q5477909
cites work: Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
cites work: Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im RaumeIIx zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen
cites work: Q3743572
cites work: On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
cites work: A factorization of regular generalized Nevanlinna functions
cites work: About generalized zeros of non-regular generalized Nevanlinna functions.
cites work: A characterization of generalized poles of generalized Nevanlinna functions
cites work: Q5840710
cites work: Q4373270
DOI: 10.1016/J.JFA.2006.09.011
description: scientific article; zbMATH DE number 5116377