Titchmarsh-Weyl theory for Schrödinger operators on unbounded domains

DOI10.4171/JST/118zbMath1381.35025arXiv1208.5224OpenAlexW2528007640MaRDI QIDQ294063

Jonathan Rohleder, Jussi Behrndt

Publication date: 9 June 2016

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5224

zbMATH Keywords

Schrödinger operatorspectrumTitchmarsh-Weyl functionDirichlet-to-Neumann map

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items

Scattering matrices and Dirichlet-to-Neumann maps, Self-adjoint Dirac operators on domains in \(\mathbb{R}^3\), Donoghue-type \(m\)-functions for Schrödinger operators with operator-valued potentials, Titchmarsh-Weyl theory for vector-valued discrete Schrödinger operators, Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Eigenvalue problems on exterior domains and Dirichlet to Neumann maps
• Spectral analysis on graph-like spaces
• Weyl function and spectral properties of self-adjoint extensions
• Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators
• An analytic characterization of the eigenvalues of self-adjoint extensions
• Boundary value problems for elliptic partial differential operators on bounded domains
• Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities
• An \(n\)-dimensional Borg-Levinson theorem
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
• On local Borg-Marchenko uniqueness results
• A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure
• The extension theory of Hermitian operators and the moment problem
• A new approach to inverse spectral theory. I: Fundamental formalism
• Simplicity of linear ordinary differential operators
• Weyl-Titchmarsh Theory for Schrodinger Operators with Strongly Singular Potentials
• A local inverse spectral theorem for Hamiltonian systems
• Square-integrable solutions and Weyl functions for singular canonical systems
• On a Problem of Weyl in the Theory of Singular Sturm-Liouville Equations
• Boundary relations and their Weyl families
• Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
• Distributions and Operators
• M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
• Eigenvalues and Pole Functions of Hamiltonian Systems with Eigenvalue Depending Boundary Conditions
• A Borg–Levinson theorem for trees
• A characterization of generalized poles of generalized Nevanlinna functions
• A proof of the local Borg-Marchenko theorem