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June 2007 Asymptotic Estimates for the Spectral Gaps of the Schrödinger Operators with Periodic $\delta^{\prime}$-Interactions
Tomohiro ICHIMURA
Tokyo J. Math. 30(1): 121-138 (June 2007). DOI: 10.3836/tjm/1184963651

Abstract

In this note we investigate the spectral gaps of the Schrödinger operator $$H=-\frac{d^2}{dx^2}+\sum_{l=-\infty}^{\infty}\big(\beta_1\delta^{\prime}(x-2\pi l)+\beta_2\delta^{\prime}(x-\kappa-2\pi l)\big) \quad \textrm{in} \quad L^2(\mathbf{R})\,,$$ where $\beta_1$, $\beta_2 \in \mathbf{R}\setminus\{0\}$ and $\kappa/\pi \in \mathbf{Q}$. By $G_{j}$ we denote the $j$-th gap of the spectrum of $H$. We provide the asymptotic expansion of the length of $G_{j}$ as $j\rightarrow\infty$.

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Tomohiro ICHIMURA. "Asymptotic Estimates for the Spectral Gaps of the Schrödinger Operators with Periodic $\delta^{\prime}$-Interactions." Tokyo J. Math. 30 (1) 121 - 138, June 2007. https://doi.org/10.3836/tjm/1184963651

Information

Published: June 2007
First available in Project Euclid: 20 July 2007

zbMATH: 1132.34063
MathSciNet: MR2328059
Digital Object Identifier: 10.3836/tjm/1184963651

Rights: Copyright © 2007 Publication Committee for the Tokyo Journal of Mathematics

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Vol.30 • No. 1 • June 2007
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