An analytic characterization of the eigenvalues of self-adjoint extensions

DOI10.1016/j.jfa.2006.09.011zbMath1114.47037OpenAlexW2145277513MaRDI QIDQ859667

Annemarie Luger, Jussi Behrndt

Publication date: 16 January 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.09.011

zbMATH Keywords

Krein spaceboundary value problemself-adjoint extension(locally) definitizable operator(locally) generalized Nevanlinna functiongeneralized pole and zeroKrein-Naimark formula

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Weyl theory and its generalizations for ordinary differential equations (34B20) Eigenvalue problems for linear operators (47A75) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Applications of operator theory to differential and integral equations (47N20) Linear operators on spaces with an indefinite metric (47B50) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (8)

Titchmarsh-Weyl theory for Schrödinger operators on unbounded domains ⋮ Generalized Nevanlinna Functions: Operator Representations, Asymptotic Behavior ⋮ Scattering theory for open quantum systems with finite rank coupling ⋮ SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS ⋮ Analytic characterizations of Jordan chains by pole cancellation functions of higher order ⋮ On the negative squares of a class of self‐adjoint extensions in Krein spaces ⋮ Boundary value problems with eigenvalue depending boundary conditions ⋮ Distributional representations of Nκ(∞)‐functions

Cites Work

• A factorization of regular generalized Nevanlinna functions
• Sturm--Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions
• On locally definitizable matrix functions
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• On compact perturbations of locally definitizable selfadjoint relations in Krein spaces
• About generalized zeros of non-regular generalized Nevanlinna functions.
• On Weyl function and generalized resolvents of a Hermitian operator in a Krein space
• The extension theory of Hermitian operators and the moment problem
• On generalized resolvents of Hermitian relations in Krein spaces
• Boundary value problems with local generalized Nevanlinna functions in the boundary condition
• Spectral points of type \(\pi_{+}\) and \(\pi_{-}\) of self-adjoint operators in Krein spaces
• Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im RaumeIIx zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen
• Sturm–Liouville problems with eigenparameter dependent boundary conditions
• Eigenvalues and Pole Functions of Hamiltonian Systems with Eigenvalue Depending Boundary Conditions
• A class of nonlinear elliptic boundary value problems
• A characterization of generalized poles of generalized Nevanlinna functions
• The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
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