99-297 IFTIMOVICI Andrei, MANTOIU Marius
Limiting Absorption Principle at Critical Values for the Dirac Operator (239K, LaTeX 2e and PostScript) Aug 13, 99
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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 $H=H_0 +V$.

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