Spectral Enclosures and Complex Resonances for General Self-Adjoint Operators

DOI10.1112/S1461157000000140zbMath0931.47021MaRDI QIDQ4230659

E. Brian Davies

Publication date: 8 February 1999

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.lms.ac.uk/jcm/1/

zbMATH Keywords

computation of eigenvalues and complex resonancesgeneral selfadjoint operatorspectrum of Schrödinger operators

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (20)

Spectral Approximation of Bounded Self-Adjoint Operators—A Short Survey ⋮ The second order spectrum and optimal convergence ⋮ Convergence of sequences of linear operators and their spectra ⋮ On the limit behaviour of second order relative spectra of self-adjoint operators ⋮ Spectral pollution and eigenvalue bounds ⋮ The foundations of spectral computations via the solvability complexity index hierarchy ⋮ On the eigenvalues of spectral gaps of elliptic PDEs on waveguides ⋮ 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 ⋮ Local two-sided bounds for eigenvalues of self-adjoint operators ⋮ Perturbation of operators and approximation of spectrum ⋮ Eigenvalue enclosures and convergence for the linearized MHD operator ⋮ On pseudospectra of matrix polynomials and their boundaries ⋮ Computation of sharp estimates of the Poincaré constant on planar domains with piecewise self-similar boundary ⋮ Enclosure results for second-order relative spectra by elementary means ⋮ Limiting set of second order spectra ⋮ On the convergence of second-order spectra and multiplicity ⋮ On the infinite-dimensional QR algorithm ⋮ A hierarchical method for obtaining eigenvalue enclosures

Cites Work

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• General lower bounds for resonances in one dimension
• Szegö type limit theorems
• On the convergence of the Goerisch method for self-adjoint eigenvalue problems with arbitrary spectrum
• Generalizations of Temple's Inequality
• The factorization problem for nonnegative operator valued functions

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