Perturbation of pseudoresolvents and analyticity in 1/c in relativistic quantum mechanics

The analytic functional calculus, relatively bounded and analytic perturbations of pseudoresolvents have been studied. As an application, the nonrelativistic limit of the Dirac and Klein-Gordon operator in the presence of an external static field has been considered. It has been proved that the resolvents of these operators have only a removable singularity atc=∞. This implies the analyticity atc=∞ of the eigenvalues and eigenvectors corresponding to the bound states of the mentioned operators.