IFTIMOVICI Andrei, MANTOIU Marius
Limiting Absorption Principle at Critical
Values for the Dirac Operator
(239K, LaTeX 2e and PostScript)
ABSTRACT. We prove estimates for the resolvent $(H_0 - z)^{-1}$
of the Dirac operator $H_0 = \alpha \cdot P + m\beta$,
valid even for $z$ close to the critical points $\pm m$.
In particular, it is shown that the operator
$(1 + |x|^{2})^{-1/2}$ is globally $H_0$-smooth.
As a by-product, the absence of the singular spectrum
as well as the existence and unitarity of the wave operators
are obtained for a class of perturbations of $H=H_0 +V$.