## Tsukuba Journal of Mathematics

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

Yorimasa Oshime

#### 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 $q(x)$.

#### Article information

Source
Tsukuba J. Math., Volume 39, Number 2 (2016), 207-220.

Dates
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.tkbjm/1461270057

Digital Object Identifier
doi:10.21099/tkbjm/1461270057

Mathematical Reviews number (MathSciNet)
MR3490485

Zentralblatt MATH identifier
1344.35016

Subjects