Elementary linear algebra for advanced spectral problems

DOI10.5802/aif.2328zbMath1140.15009arXivmath/0312166OpenAlexW1481378894MaRDI QIDQ2477555

Publication date: 14 March 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312166

zbMATH Keywords

eigenvalues Schur complement resonances Poisson summation formula trace formulae Grushin problem feshback reduction

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10) PDEs in connection with quantum mechanics (35Q40) Perturbation theories for operators and differential equations in quantum theory (81Q15) Canonical forms, reductions, classification (15A21)

Related Items

Hypocoercivity with Schur complements ⋮ On the spectrum of some Bloch-Torrey vector operators ⋮ The Fermi golden rule and its form at thresholds in odd dimensions ⋮ Interior Eigenvalue Density of Jordan Matrices with Random Perturbations ⋮ Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations ⋮ Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics ⋮ Distribution of resonances for open quantum maps ⋮ Sharp spectral asymptotics for nonreversible metastable diffusion processes ⋮ Magnetic oscillations in a model of graphene ⋮ A probabilistic Weyl-law for perturbed Berezin-Toeplitz operators ⋮ Almost sure Weyl law for quantized tori ⋮ The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems ⋮ Boundedness of metaplectic Toeplitz operators and Weyl symbols ⋮ On perturbation of operators and Rayleigh-Schrödinger coefficients ⋮ Fractal Weyl law for open quantum chaotic maps ⋮ Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations ⋮ Low-lying eigenvalues and convergence to the equilibrium of some piecewise deterministic Markov processes generators in the small temperature regime ⋮ Toeplitz band matrices with small random perturbations ⋮ Hypoellipticity and higher order Levi conditions ⋮ General Toeplitz matrices subject to Gaussian perturbations ⋮ Spectral analysis of a two body problem with zero-range perturbation ⋮ Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators ⋮ Eigenvalues and eigenfunctions for the two dimensional Schrödinger operator with strong magnetic field ⋮ The precise shape of the eigenvalue intensity for a class of non-self-adjoint operators under random perturbations ⋮ Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells. I ⋮ Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries ⋮ Two point eigenvalue correlation for a class of non-selfadjoint operators under random perturbations ⋮ From open quantum systems to open quantum maps ⋮ Microlocal analysis of the bulk-edge correspondence ⋮ Local eigenvalue statistics of one-dimensional random nonselfadjoint pseudodifferential operators ⋮ Probabilistic Weyl laws for quantized tori ⋮ PT-symmetry and Schrödinger operators. The double well case ⋮ Spectral statistics of non-selfadjoint operators subject to small random perturbations ⋮ Normal form of equivariant maps in infinite dimensions ⋮ Spectral properties and time decay of the wave functions of Pauli and Dirac operators in dimension two ⋮ On the spectrum of an anharmonic oscillator ⋮ Deterministic equivalence for noisy perturbations ⋮ Scattering resonances of convex obstacles for general boundary conditions ⋮ Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator ⋮ Dynamics of resonances for 0th order pseudodifferential operators

Cites Work