The extension theory of Hermitian operators and the moment problem

DOI10.1007/BF02367240zbMath0848.47004MaRDI QIDQ1910820

Vladimir A. Derkach, Mark M. Malamud

Publication date: 23 April 1996

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

zbMATH Keywords

Weyl function\(R\)-functionextension theoryresolvent matricesgeneralized resolventsholomorphic operator-valued functionnondensely defined Hermitian operatorpreresolventresolvent matrix of a Hermitian operatortruncated Hamburger, Stieltjes and Hausdorff moment problems

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) 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) Dilations, extensions, compressions of linear operators (47A20)

Related Items (only showing first 100 items - show all)

Sturm--Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions ⋮ Trace formulas for additive and non-additive perturbations ⋮ Scattering matrices and Dirichlet-to-Neumann maps ⋮ M-dissipative boundary conditions and boundary tuples for Maxwell operators ⋮ Titchmarsh-Weyl theory for Schrödinger operators on unbounded domains ⋮ Darboux transformation with parameter of generalized Jacobi matrices ⋮ Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators ⋮ Dirichlet-to-Neumann maps, abstract Weyl-Titchmarsh \(M\)-functions, and a generalized index of unbounded meromorphic operator-valued functions ⋮ An Inverse Problem of Calderón Type with Partial Data ⋮ Spectral theory for perturbed Krein Laplacians in nonsmooth domains ⋮ Boundary triples for integral systems on finite intervals ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ An analytic characterization of the eigenvalues of self-adjoint extensions ⋮ Spectral shift functions and Dirichlet-to-Neumann maps ⋮ A note on Wall's modification of the Schur algorithm and linear pencils of Jacobi matrices ⋮ Unitary boundary pairs for isometric operators in Pontryagin spaces and generalized coresolvents ⋮ A truncated indefinite Stieltjes moment problem ⋮ Accretive and sectorial extensions of nonnegative symmetric operators ⋮ Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator ⋮ Elliptic boundary value problems with \(\lambda \)-dependent boundary conditions ⋮ Boundary value problems for elliptic partial differential operators on bounded domains ⋮ Similarity of some \(J\)-nonnegative operators to self-adjoint operators ⋮ On the Kato-Rosenblum and Weyl-von Neumann theorems ⋮ A functional model associated with a generalized Nevanlinna pair ⋮ Spectral analysis of selfadjoint elliptic differential operators, Dirichlet-to-Neumann maps, and abstract Weyl functions ⋮ An operator approach to the indefinite Stieltjes moment problem ⋮ Rigged de Branges-Pontryagin spaces and their application to extensions and embedding ⋮ Spectral estimates for resolvent differences of self-adjoint elliptic operators ⋮ Spectral transition for Dirac operators with electrostatic \(\delta\)-shell potentials supported on the straight line ⋮ To the theory of nonnegative point Hamiltonians on a plane and in the space ⋮ On the unitary equivalence of absolutely continuous parts of self-adjoint extensions ⋮ On compressions of self-adjoint extensions of a symmetric linear relation ⋮ Two-dimensional Dirac operators with singular interactions supported on closed curves ⋮ Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\) ⋮ Scattering theory for open quantum systems with finite rank coupling ⋮ On the spectral properties of Dirac operators with electrostatic \(\delta\)-shell interactions ⋮ Eigenvalue estimates for operators with finitely many negative squares ⋮ Non-relativistic limit for matrix 1D-Dirac operators with point interactions ⋮ The Jacobi matrices approach to Nevanlinna-Pick problems ⋮ Sturm-Liouville boundary value problems with operator potentials and unitary equivalence ⋮ Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces ⋮ Representations of unitary relations between Kreĭn spaces ⋮ On spectral theory for Schrödinger operators with operator-valued potentials ⋮ On the unitary equivalence of the proper extensions of a Hermitian operator and the Weyl function ⋮ Symmetric operators with real defect subspaces of the maximal dimension. Applications to differential operators ⋮ Pseudospectral functions of various dimensions for symmetric systems with the maximal deficiency index ⋮ An example of unitary equivalence between self-adjoint extensions and their parameters ⋮ On Titchmarsh-Weyl functions and eigenfunction expansions of first-order symmetric systems ⋮ Unitary equivalence of proper extensions of a symmetric operator and the Weyl function ⋮ Products of generalized Nevanlinna functions with symmetric rational functions ⋮ Functional models for entire symmetric operators in rigged de Branges Pontryagin spaces ⋮ Elliptic differential operators on Lipschitz domains and abstract boundary value problems ⋮ On Eisenbud's and Wigner's \(R\)-matrix: A general approach ⋮ Non-compact quantum graphs with summable matrix potentials ⋮ \(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮ On generalized resolvents of Hermitian relations in Krein spaces ⋮ Non-self-adjoint extensions of a Hermitian operator and their characteristic functions ⋮ Compressed resolvents and reduction of spectral problems on star graphs ⋮ Restrictions and extensions of semibounded operators ⋮ Deficiency indices and discreteness property of block Jacobi matrices and Dirac operators with point interactions ⋮ On a class of integral systems ⋮ Variations on a theme of Jost and Pais ⋮ Coupling of symmetric operators and the third Green identity ⋮ Dissipative extension theory for linear relations ⋮ Boundary triplets for skew symmetric operators and the generation of strongly continuous semigroups ⋮ 1-D Schrödinger operators with local interactions on a discrete set with unbounded potential ⋮ Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\) ⋮ Donoghue-type \(m\)-functions for Schrödinger operators with operator-valued potentials ⋮ Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations ⋮ Spectral theory of elliptic operators in exterior domains ⋮ Weyl function and spectral properties of self-adjoint extensions ⋮ A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains ⋮ Shifted Darboux transformations of the generalized Jacobi matrices. I ⋮ 1-D Schrödinger operators with local point interactions on a discrete set ⋮ Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures ⋮ On the criteria of transversality and disjointness of nonnegative self-adjoint extensions of nonnegative symmetric operators ⋮ Boundary triplets, tensor products and point contacts to reservoirs ⋮ A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains ⋮ Dirac structures and their composition on Hilbert spaces ⋮ On the negative squares of indefinite Sturm--Liouville operators ⋮ On symmetries in the theory of finite rank singular perturbations ⋮ Multi-dimensional versions of a determinant formula due to Jost and Pais ⋮ Partially fundamentally reducible operators in Kreĭn spaces ⋮ On Kreĭn's formula ⋮ Spectral multiplicity of selfadjoint Schrödinger operators on star-graphs with standard interface conditions ⋮ Square-integrable solutions and Weyl functions for singular canonical systems ⋮ The wave model of the Sturm-Liouville operator on an interval ⋮ An addendum to Krein's formula ⋮ Approximate controllability of the wave equation with mixed boundary conditions ⋮ Extensions of Laguerre operators in indefinite inner product spaces ⋮ Boundary relations and generalized resolvents of symmetric operators ⋮ Spectral problems for generalized Jacobi matrices ⋮ On functions connected with sectorial operators and their extensions ⋮ Boundary-value problems for two-dimensional canonical systems ⋮ Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps ⋮ Inverse spectral theory for symmetric operators with several gaps: scalar-type Weyl functions ⋮ m-Accretive extensions of a sectorial operator ⋮ Perturbation determinants for singular perturbations ⋮ Rank one perturbations in a Pontryagin space with one negative square ⋮ Completion, extension, factorization, and lifting of operators

Cites Work

• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Asymptotic behavior of integral functionals of diffusion processes with periodic coefficients
• Characteristic functions of almost solvable extensions of Hermitian operators
• A generalization of a class of Krein-Stieltjes functions
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
• On a formula of the generalized resolvents of a nondensely defined Hermitian operator
• On generalized resolvents of Hermitian operators in Krein spaces
• THE THEORY OF BI-EXTENSIONS OF OPERATORS ON RIGGED HILBERT SPACES. UNBOUNDED OPERATOR COLLIGATIONS AND CHARACTERISTIC FUNCTIONS
• Characteristic functions of linear operators
• EXTENSIONS AND GENERALIZED RESOLVENTS OF A SYMMETRIC OPERATOR WHICH IS NOT DENSELY DEFINED
• Defect subspaces and generalized resolvents of an Hermitian operator in the space \(\Pi_\kappa\)
• 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
• 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: The extension theory of Hermitian operators and the moment problem