Spectral instabilities: variations on a theme loved by Brian Davies

Perturbation theory of linear operators (47A55) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Spectral sets of linear operators (47A25) Toeplitz, Cauchy, and related matrices (15B05)

Cites Work

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Spectrum of a Feinberg-Zee random hopping matrix
Toeplitz determinants with perturbations in the corners
Algebraic methods for Toeplitz-like matrices and operators
Eigenvalue clusters of large tetradiagonal Toeplitz matrices
New barriers in complexity theory: on the solvability complexity index and the towers of algorithms
Perturbations of Jordan matrices
Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
Spectral properties of Neumann Laplacian of horns
Toeplitz operators with semialmost periodic symbols
Introduction to large truncated Toeplitz matrices
The Fisher-Hartwig conjecture and Toeplitz eigenvalues
Pseudospectra and singular values of large convolution operators
Infinite Toeplitz and Laurent matrices with localized impurities
On the continuity of spectra of Toeplitz operators
Eigenvalues of an elliptic system
Asymptotic spectra of dense Toeplitz matrices are unstable
Spectral instability for some Schrödinger operators
The spectrum is discontinuous on the manifold of Toeplitz operators
Some results on complex Toeplitz eigenvalues
Spectral stability of the Neumann Laplacian.
Non-Weyl resonance asymptotics for quantum graphs
On the approximation of spectra of linear operators on Hilbert spaces
Spectral properties of random non-self-adjoint matrices and operators
On the Solvability Complexity Index, the 𝑛-pseudospectrum and approximations of spectra of operators
The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices
NON-SELF-ADJOINT DIFFERENTIAL OPERATORS
The Toeplitz Matrices of an Arbitrary Laurent Polynomial.
A Defence of Mathematical Pluralism
LEVEL SETS OF THE RESOLVENT NORM OF A LINEAR OPERATOR REVISITED
On the level sets of the resolvent norm of a linear operator
Approximate Diagonalization
Pseudo–spectra, the harmonic oscillator and complex resonances
Wild Spectral Behaviour of Anharmonic Oscillators
Complexity issues in computing spectra, pseudospectra and resolvents
Hyponormality and spectra of Toeplitz operators
Piecewise Continuous Toeplitz Matrices and Operators: Slow Approach to Infinity
Spectral pollution
On the Problem of Testing the Structure of a Matrix by Displacement Operations
Spectral Properties of Banded Toeplitz Matrices
Spectral approximation of banded Laurent matrices with localized random perturbations

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