Band gap of the Schroedinger operator with a strong delta-interaction on a periodic curve

Pavel Exner, Kazushi Yoshitomi

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…