Abstract
Schrödinger operators $T_0 = -\Delta + q(x)$ with rapidly oscillating complex-valued potentials $q(x)$ are considered. Each of such operators is sectorial and hence has Friedrichs extension. We prove that $T_0$ is essentially m-sectorial in the sense that the closure of $T_0$ coincides with its Friedrichs extension $T$. In particular, $T_0$ is essentially self-adjoint if the rapidly oscillating potential $q(x)$ is realvalued. Further, we prove $\sigma_{ess} (T) = [0, \infty)$ under somewhat stricter condition on the potentials $q(x)$.
Citation
Yorimasa Oshime. "Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials." Tsukuba J. Math. 39 (2) 207 - 220, March 2016. https://doi.org/10.21099/tkbjm/1461270057
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