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

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

2009-06-08

arxiv.org/abs/0906.1495v1

Mathematics

Analysis of PDEs

Scientific paper

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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