Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies

Abstract

We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of non-self-adjoint operators. The technique is based on a positive commutator theory for non self-adjoint operators, which we develop in appendix. We also discuss some applications to the dispersive Helmholzt model in the quantum regime.

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Cited by in corpus (11)

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• Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions
• Scattering theory for Lindblad master equations
• Dispersive estimates for massive Dirac operators in dimension two
• On the Global Limiting Absorption Principle for Massless Dirac Operators
• Limiting Absorption Principle for Schrödinger Operators with Oscillating Potential
• On the a.c. spectrum of 1D discrete Dirac operator
• Diffraction for the Dirac-Coulomb propagator
• Mourre's method for a dissipative form perturbation
• The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions
• Spectral theory of first-order systems: from crystals to Dirac operators