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March 2016 Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials
Yorimasa Oshime
Tsukuba J. Math. 39(2): 207-220 (March 2016). DOI: 10.21099/tkbjm/1461270057

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 $q(x)$.

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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

Information

Published: March 2016
First available in Project Euclid: 21 April 2016

zbMATH: 1344.35016
MathSciNet: MR3490485
Digital Object Identifier: 10.21099/tkbjm/1461270057

Subjects:
Primary: 35J10
Secondary: 35P15

Rights: Copyright © 2016 University of Tsukuba, Institute of Mathematics

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Vol.39 • No. 2 • March 2016
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