Eigenvalues in spectral gaps of differential operators

DOI10.4171/JST/30zbMath1256.65079WikidataQ115180772 ScholiaQ115180772MaRDI QIDQ442470

Robert Scheichl, Marco Marlettta

Publication date: 11 August 2012

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

zbMATH Keywords

discretizationeigenvaluesSchrödinger equationessential spectrumspectral gapvariational methoddissipativeself-adjoint operatorsSchrödingerspectral bandspectral pollution

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (18)

Bounds for Schrödinger operators on the half-line perturbed by dissipative barriers ⋮ Numerical computation of eigenvalues in spectral gaps of Schrödinger operators ⋮ The foundations of spectral computations via the solvability complexity index hierarchy ⋮ On the eigenvalues of spectral gaps of elliptic PDEs on waveguides ⋮ Lieb-Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line ⋮ Spectral enclosure and superconvergence for eigenvalues in gaps ⋮ Eigenvalues computation by the generalized spectrum method of Schrödinger's operator ⋮ A new approach to spectral approximation ⋮ On the eigenvalues of spectral gaps of matrix-valued Schrödinger operators ⋮ The Galerkin method for perturbed self-adjoint operators and applications ⋮ Non-consistent approximations of self-adjoint eigenproblems: application to the supercell method ⋮ Spectral inclusion and pollution for a class of dissipative perturbations ⋮ Computing spectral measures and spectral types ⋮ Computation of sharp estimates of the Poincaré constant on planar domains with piecewise self-similar boundary ⋮ Pseudoergodic operators and periodic boundary conditions ⋮ On the infinite-dimensional QR algorithm ⋮ THE FINITE SECTION METHOD FOR DISSIPATIVE OPERATORS ⋮ An algorithm for identifying eigenvectors exhibiting strong spatial localization

Cites Work

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• A perfectly matched layer for the absorption of electromagnetic waves
• On spectral pollution in the finite element approximation of thin elastic ``membrane shells
• Spectral instability for some Schrödinger operators
• Critical coupling constants and eigenvalue asymptotics of perturbed periodic Sturm-Liouville operators
• Variational bounds to eigenvalues of selfadjoint eigenvalue problems with arbitrary spectrum
• Approximation of isolated eigenvalues of general singular ordinary differential operators
• Regular approximations of singular Sturm-Liouville problems
• The spectrum of a periodic operator with a small localized perturbation
• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• Neumann-Dirichlet maps and analysis of spectral pollution for non-self-adjoint elliptic PDEs with real essential spectrum
• Spectral pollution and how to avoid it
• Convergence of regular approximations to the spectra of singular fourth-order Sturm–Liouville problems
• On the spectrum of second-order differential operators with complex coefficients
• Spectral Concentration for Perturbed Equations of Harmonic Oscillator Type
• Spectral pollution and second-order relative spectra for self-adjoint operators
• Spectral pollution
• The Newton-Kantorovich Theorem
• On approximation of the eigenvalues of perturbed periodic Schrödinger operators

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