Spectral gaps of the one-dimensional Schrödinger operators with periodic point interactions
type: Item
instance of: scholarly article
title: Spectral gaps of the one-dimensional Schrödinger operators with periodic point interactions
zbMATH Open document ID: 1114.34067
author: Kazushi Yoshitomi
published in: Hokkaido Mathematical Journal
publication date: 2006-11-29T00:00:00Z
review text: The spectral gaps of the Schrödinger operators \[ H_{1}=-\frac{d^{2}}{dx^{2}}+\sum^{\infty}_{l=-\infty}( \beta_{1}\delta^{\prime}(x-\kappa-2\pi l)+\beta_{2}\delta^{\prime}(x-2\pi l))\quad \text{ in}\quad L^{2}({\mathbb R}), \] \[ H_{2}=-\frac{d^{2}}{dx^{2}}+\sum^{\infty}_{l=-\infty}( \beta_{1}\delta(x-\kappa-2\pi l)+\beta_{2}\delta(x-2\pi l))\quad \text{ in}\quad L^{2}({\mathbb R}), \] are studied, where \(\kappa\in (0,2\pi)\) and \(\beta_{1},\beta_{2}\in{\mathbb R}\backslash\{0\}\) are parameters. Given \(j\in{\mathbb N}\), it is determined that the \(j\)th gap of \(H_{k}\) is absent or not for \(k=1,2\).
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 5076741
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: periodic point interactions
zbMATH Keywords: spectral gaps
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1285766361
OpenAlex ID: W1968555618
DOI: 10.14492/HOKMJ/1285766361
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description: scientific article; zbMATH DE number 5076741