Spectral estimates for resolvent differences of self-adjoint elliptic operators

DOI10.1007/s00020-013-2072-2zbMath1311.47059arXiv1012.4596OpenAlexW2003897227MaRDI QIDQ395610

Vladimir Lotoreichik, Jussi Behrndt, Matthias Langer

Publication date: 29 January 2014

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.4596

zbMATH Keywords

elliptic operatorWeyl functionoperator idealself-adjoint extension\(\delta\)-potentialquasi boundary triple

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Operator ideals (47L20)

Related Items (12)

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces ⋮ Scattering matrices and Dirichlet-to-Neumann maps ⋮ Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ Spectral shift functions and Dirichlet-to-Neumann maps ⋮ On the spectral properties of Dirac operators with electrostatic \(\delta\)-shell interactions ⋮ Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces ⋮ Scattering matrices and Weyl functions of quasi boundary triples ⋮ Elliptic differential operators on Lipschitz domains and abstract boundary value problems ⋮ Scattering of particles bounded to an infinite planar curve ⋮ Coupling of symmetric operators and the third Green identity ⋮ Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems

Cites Work

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• A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains
• \(M\) operators: A generalisation of Weyl--Titchmarsh theory
• Elliptic boundary value problems with \(\lambda \)-dependent boundary conditions
• Spectral analysis on graph-like spaces
• The Dirichlet-to-Neumann operator on rough domains
• Weyl function and spectral properties of self-adjoint extensions
• Singular Green operators and their spectral asymptotics
• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• Boundary value problems for elliptic partial differential operators on bounded domains
• The local and global parts of the basic zeta coefficient for operators on manifolds with boundary
• Spectral theory of elliptic operators in exterior domains
• 1-D Schrödinger operators with local point interactions on a discrete set
• A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains
• Impedance passive and conservative boundary control systems
• Weyl-Titchmarsh function of an abstract boundary value problem, operator colligations, and linear systems with boundary control
• Variation of discrete spectra
• 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
• Schrödinger operators with singular interactions
• Singular perturbations of self-adjoint operators
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Perturbation theory for linear operators.
• The extension theory of Hermitian operators and the moment problem
• Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces
• Extension theory and Kreĭn-type resolvent formulas for nonsmooth boundary value problems
• Spectral asymptotics for Robin problems with a discontinuous coefficient
• Geometrically induced spectrum in curved leaky wires
• Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators
• On a formula of the generalized resolvents of a nondensely defined Hermitian operator
• Remarks on trace estimates for exterior boundary problems
• Boundary relations and their Weyl families
• Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
• Scattering matrices and Weyl functions
• Leaky Quantum Graphs: A Review
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains
• Bound states due to a strong   interaction supported by a curved surface
• Non-Local Boundary Value Problems for Elliptic Operators
• Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators
• Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• The Resolvent of an Elliptic Boundary Problem

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