 01226 Pavel Exner, Kazushi Yoshitomi
 Band gap of the Schroedinger operator with a strong
deltainteraction on a periodic curve
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Jun 25, 01

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Abstract. In this paper we study the operator
$H_{\beta}=\Delta\beta\delta(\cdot\Gamma)$ in
$L^{2}(\mathbb{R}^{2})$, where $\Gamma$ is a smooth periodic curve
in $\mathbb{R}^{2}$. We obtain the asymptotic form of the band
spectrum of $H_{\beta}$ as $\beta$ tends to infinity. Furthermore,
we prove the existence of the band gap of $\sigma(H_{\beta})$ for
sufficiently large $\beta>0$. Finally, we also derive the spectral
behaviour for $\beta\to\infty$ in the case when $\Gamma$ is
nonperiodic and asymptotically straight.
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