On generalized resolvents of Hermitian relations in Krein spaces

DOI10.1007/BF02366102zbMath0955.47022MaRDI QIDQ1971743

Vladimir A. Derkach

Publication date: 28 March 2000

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

zbMATH Keywords

Krein spaceWeyl functiongeneralized resolventoperator-valued functiontruncated moment problemboundary-value spacedefinitizableHermitian linear relation

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator methods in interpolation, moment and extension problems (47A57) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Linear relations (multivalued linear operators) (47A06) Linear operators on spaces with an indefinite metric (47B50)

Related Items (30)

Sturm--Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions ⋮ Boundary Triplets, Weyl Functions, and the Kreĭn Formula ⋮ Borg-type theorems for generalized Jacobi matrices ⋮ An analytic characterization of the eigenvalues of self-adjoint extensions ⋮ Unitary boundary pairs for isometric operators in Pontryagin spaces and generalized coresolvents ⋮ Realization of nonstrict matrix Nevanlinna functions as Weyl functions of symmetric operators in Pontryagin spaces ⋮ Elliptic boundary value problems with \(\lambda \)-dependent boundary conditions ⋮ Boundary value problems for elliptic partial differential operators on bounded domains ⋮ An operator approach to the indefinite Stieltjes moment problem ⋮ Rigged de Branges-Pontryagin spaces and their application to extensions and embedding ⋮ Weyl families of transformed boundary pairs ⋮ On the similarity of boundary triples of symmetric operators in Krein spaces ⋮ Indefinite Sturm-Liouville operators in polar form ⋮ Bessel-type operators with an inner singularity ⋮ SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS ⋮ Description of scattering matrices of unitary extensions of isometric operators in Pontryagin space ⋮ On the convergence of Padé approximations for generalized Nevanlinna functions ⋮ Functional models for entire symmetric operators in rigged de Branges Pontryagin spaces ⋮ Factorization of \(J\)-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions ⋮ Truncated moment problems in the class of generalized Nevanlinna functions ⋮ Generalized Jacobi operators in Krein spaces ⋮ On the negative squares of a class of self‐adjoint extensions in Krein spaces ⋮ Resolvent convergence and spectral approximations of sequences of self-adjoint subspaces ⋮ The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces ⋮ On the negative squares of indefinite Sturm--Liouville operators ⋮ Boundary value problems with eigenvalue depending boundary conditions ⋮ Spectral problems for generalized Jacobi matrices ⋮ Distributional representations of Nκ(∞)‐functions ⋮ Operator-based approach to \({\mathcal{P}}{\mathcal{T}}\)-symmetric problems on a wedge-shaped contour ⋮ Standard symmetric operators in Pontryagin spaces: A generalized von Neumann formula and minimality of boundary coefficients

Cites Work

• L-resolvent matrices of symmetric linear relations with equal defect numbers; applications to canonical differential relations
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Self-adjoint extensions of symmetric subspaces
• On generalized resolvents and \(Q\)-functions of symmetric linear relations (subspaces) in Hilbert space
• 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 Indefinite Moment Problems and Resolvent Matrices of Hermitian Operators in Kreîn Spaces
• On a formula of the generalized resolvents of a nondensely defined Hermitian operator
• Matrix Functions of the ClassNϰ
• Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im RaumeIIx zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen
• Fundamental aspects of the representation theory of Hermitian operators with deficiency index (𝑚,𝑚)
• Extension theory of formally normal and symmetric subspaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On generalized resolvents of Hermitian relations in Krein spaces