Towards spectral theory of the Nonstationary Schr\"{o}dinger equation with a two-dimensionally perturbed one-dimensional potential

Abstract

The Nonstationary Schr\"{o}dinger equation with potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function is considered here in the framework of the extended resolvent approach. The properties of the Jost solutions and spectral data are investigated.Comment: 22 pages, no figure