Tsukuba Journal of Mathematics

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

Yorimasa Oshime

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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

Permanent link to this document
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
Primary: 35J10: Schrödinger operator [See also 35Pxx]
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds

Keywords
Oscillating potentials Sectorial forms Friedrichs extension

Citation

Oshime, Yorimasa. Essential m-sectoriality and essential spectrum of the Schrödinger operators with rapidly oscillating complex-valued potentials. Tsukuba J. Math. 39 (2016), no. 2, 207--220. doi:10.21099/tkbjm/1461270057. https://projecteuclid.org/euclid.tkbjm/1461270057


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