Spectrum of the nonself-adjoint Schr�dinger operator in unbounded regions

Abstract

It is proved that the discrete spectrum of the operator −Δ + q(x) in the space L2(E2k) (k ≥1) where q(x) is a measurable complex-valued function satisfying the condition ¦q(x) ¦ ≤Ce−ɛ¦x¦, having no finite limit points, and for k=1 the discrete spectrum consists of a finite number of points.