Pseudomodes for non-self-adjoint Dirac operators

Abstract

Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic approach which goes beyond the standard semi-classical setting. Furthermore, this approach results in substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including superexponential ones.