Characteristic functions of almost solvable extensions of Hermitian operators

DOI10.1007/BF01064871zbMath0804.47009MaRDI QIDQ1198905

Vladimir A. Derkach, Mark M. Malamud

Publication date: 16 January 1993

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

inverse problemWeyl functioncharacteristic operator functionboundary operatormultiplication theoremalmost solvable extension of an Hermitian operatorcompleteness theorems for systems of eigen- and associated vectors

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Dilations, extensions, compressions of linear operators (47A20) Canonical models for contractions and nonselfadjoint linear operators (47A45)

Related Items (17)

Trace formulas for additive and non-additive perturbations ⋮ Minimal spectral functions of an ordinary differential operator ⋮ Krein-von Neumann extension of an even order differential operator on a finite interval ⋮ On Weyl function and generalized resolvents of a Hermitian operator in a Krein space ⋮ The extension theory of Hermitian operators and the moment problem ⋮ Discrete symplectic systems, boundary triplets, and self-adjoint extensions ⋮ Scattering theory for 0-perturbed \(\mathcal{PT}\)-symmetric operators ⋮ The functional model for maximal dissipative operators (translation form): An approach in the spirit of operator knots ⋮ Linear Operators and Operator Functions Associated with Spectral Boundary Value Problems ⋮ Description of generalized resolvents and characteristic matrices of differential operators in terms of the boundary parameter ⋮ Symmetric operators with real defect subspaces of the maximal dimension. Applications to differential operators ⋮ Unitary equivalence of proper extensions of a symmetric operator and the Weyl function ⋮ Non-self-adjoint extensions of a Hermitian operator and their characteristic functions ⋮ Krein extension of an even-order differential operator ⋮ On the perturbation theory of self-adjoint operators ⋮ Boundary relations and generalized resolvents of symmetric operators ⋮ Perturbation determinants for singular perturbations

Cites Work

• Extension theory for symmetric operators and boundary value problems for differential equations
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Self-adjoint extensions of symmetric subspaces
• Non-self-adjoint extensions of a Hermitian operator and their characteristic functions
• Description of contraction operators which are similar to unitary operators
• Discrete and continuous boundary problems
• Operators satisfying smoothness conditions
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