Abstract
This is the first part of a series of two papers, which investigate spectral properties of Dirac operators with singular poten- tials. We examine various properties of complex dilated Dirac oper- ators. These operators arise in the investigation of resonances using the method of complex dilations. We generalize the spectral analysis of Weder (50) and y (46) to operators with Coulomb type poten- tials, which are not relatively compact perturbations. Moreover, we define positive and negative spectral projections as well as transforma- tion functions between different spectral subspaces and investigate the non-relativistic limit of these operators. We will apply these results in (30) in the investigation of resonances in a relativistic Pauli-Fierz model, but they might also be of independent interest.
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