Pseudomodes for Schroedinger operators with complex potentials

Abstract

For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones.

33 pages; appendix proving technical lemmata added; version accepted for publication in Journal of Functional Analysis