Limiting absorption principle and resonances for the Dirac operator

DOI10.1016/0196-8858(92)90009-LzbMath0756.35062MaRDI QIDQ1197395

Bernard Helffer, Erik Balslev

Publication date: 16 January 1993

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

scattering matrixstationary scattering theoryspace of resonance functions

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) (2)-body potential quantum scattering theory (81U05) Scattering theory of linear operators (47A40)

Related Items (27)

High‐energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and application ⋮ Time delay for the Dirac equation ⋮ Resonances for the radial Dirac operators ⋮ Complex Absorbing Potential Method for the Perturbed Dirac Operator ⋮ High-energy behavior of the scattering amplitude for a Dirac operator ⋮ Limiting absorption principle and scattering matrix for Dirac operators with δ-shell interactions ⋮ Time evolution for the Pauli-Fierz operator (Markov approximation and Rabi cycle) ⋮ Dispersive estimates for massive Dirac operators in dimension two ⋮ Eigenvalues and resonances of Dirac operators with dilation analytic potentials diverging at infinity ⋮ Resonances for 1D massless Dirac operators ⋮ Asymptotics of the scattering phase for the Dirac operator: high energy, semi-classical and non-relativistic limits ⋮ Spectral theory of Dirac operators with potentials diverging at infinity ⋮ Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions ⋮ Some new results about the massless Dirac operator ⋮ EIGENFUNCTIONS AT THE THRESHOLD ENERGIES OF MAGNETIC DIRAC OPERATORS ⋮ Spectral theory of first-order systems: From crystals to Dirac operators ⋮ Limiting absorption principle and resonances for the Dirac operator ⋮ Resonances for Dirac operators on the half-line ⋮ Propagation estimates for Dirac operators and application to scattering theory. ⋮ Unnamed Item ⋮ On the global limiting absorption principle for massless Dirac operators ⋮ Stable directions for small nonlinear Dirac standing waves ⋮ On spectral stability of the nonlinear Dirac equation ⋮ Unnamed Item ⋮ Asymptotic expansion of the scattering phase with high energy for the Dirac operator ⋮ Unnamed Item ⋮ Scattering amplitude for dirac operators

Cites Work

• On the point spectrum of Dirac operators
• Limiting absorption principle and resonances for the Dirac operator
• Eigenfunction expansions and scattering theory for Dirac operators
• Analytic scattering theory of two-body Schrödinger operators
• Perturbation theory for linear operators.
• Perturbation of pseudoresolvents and analyticity in \(1/c\) in relativistic quantum mechanics
• Résonances en limite semi-classique
• The Singular Spectrum of Elliptic Differential Operators in $L^p (R_n)$.
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