Abstract. We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential V lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the L 1 -norm of V is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.
In this paper we establish criteria for the existence and uniqueness of contractive solutions K of the Riccati equation KBK+KA&DK&C=0 under the assumption that the spectra of A and D are disjoint.
Academic Press
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