Schrödinger operators with complex singular potentials
We study one-dimensional Schrödinger operators S(q) on the space L^2(R) with potentials q being complex-valued generalized functions from the negative space H_unif ^-1(R). Particularly the class H_unif ^-1(R) contains periodic and almost periodic H_loc ^-1(R)-functions. We establish an equivalence of the various definitions of the operators S(q), investigate their approximation by operators with smooth potentials from the space L_unif ^1(R) and prove that the spectrum of each operator S(q) lies within a certain parabola., number=1, journal=Methods of Functional Analysis and Topology, author=Molyboga, V. M. and Mikhailets, V. A., year=2013, month=Mar., pages=16–28