The periodic Dirac operator is absolutely continuous
type: Item
instance of: scholarly article
title: The periodic Dirac operator is absolutely continuous
zbMATH Open document ID: 0937.35032
DOI: 10.1007/BF01272881
published in: Integral Equations and Operator Theory
publication date: 2000-05-23T00:00:00Z
review text: The absolute continuity of the periodic Dirac Operator with a magnetic potential is shown. In the \(d=2\) dimensional case it is only necessary to require the condition that the magnetic potential is \(L_r\) \((r>2)\). Here the results and techniques shown in a previous paper of the authors are used. For the \(d=3\) and higher dimensional case other techniques, developed by Sobolev, are used and those require that the magnetic potential is \(C_{2d+3}\). Several particular results and special cases of this complete proof are shown and discussed.
reviewed by: Thoralf Chrobok
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 1340272
zbMATH Keywords: Dirac operator
zbMATH Keywords: Schrödinger operator
author: M. Sh. Birman
author: T. A. Suslina
MaRDI profile type: Publication
cites work: Spectrum of the Dirac operator in \({\mathbb{R}}^ n\) with periodic potential
cites work: Q4853529
cites work: Floquet theory for partial differential equations
cites work: Q4066072
description: scientific article; zbMATH DE number 1340272