Periodic potentials for which all gaps are nontrivial
type: Item
instance of: scholarly article
title: Periodic potentials for which all gaps are nontrivial
zbMATH Open document ID: 0907.34068
DOI: 10.1007/BF02466003
author: M. M. Senatorov
author: V. A. Geiler
publication date: 1998-10-11T00:00:00Z
review text: The authors consider the selfadjoint periodic Schrödinger operator \(H\) (i.e., Hill operator) defined as the closure in \(L^2 (\mathbb{R})\) of the symmetric operator \(-y''+ U(x)y\) on \(C_0^{\infty}(\mathbb{R})\), where \(U(x)\) is a \(2T\)-periodic square integrable function on the closed interval \([-T, T]\). The operator \(H\) has an absolutely continuous spectrum consisting of a sequence of closed intervals separated by gaps. It is proved that all gaps in the spectrum of \(H\) are nontrivial if the nonconstant \(2T\)-periodic function \(U\) defined on \([-T, T]\) extends to be an even real-analytic convex function on the whole real axis.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 1179574
zbMATH Keywords: Hill operator
zbMATH Keywords: periodic potential
zbMATH Keywords: gaps in the spectrum
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
cites work: Q4185363
cites work: Gaps and bands of one dimensional periodic Schrödinger operators
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1179574