Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials

Schrödinger operators T0 1⁄4 sþ qðxÞ with rapidly oscillating complex-valued potentials qðxÞ are considered. Each of such operators is sectorial and hence has Friedrichs extension. We prove that T0 is essentially m-sectorial in the sense that the closure of T0 coincides with its Friedrichs extension T . In particular, T0 is essentially self-adjoint if the rapidly oscillating potential qðxÞ is realvalued. Further, we prove sessðTÞ 1⁄4 1⁄20;yÞ under somewhat stricter condition on the potentials qðxÞ.