Approximating spectral invariants of Harper operators on graphs

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dc.contributor.authorVarghese, M.
dc.contributor.authorYates, S.
dc.date.issued2002
dc.description.abstractWe study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada (Sun). A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs with a free action of an amenable discrete group can be approximated by the average spectral density function of the DMLs on a regular exhaustion, with either Dirichlet or Neumann boundary conditions. This then gives a criterion for the existence of gaps in the spectrum of the DML, as well as other interesting spectral properties of such DMLs. The technique used incorporates some results of algebraic number theory.
dc.description.statementofresponsibilityVarghese Mathai and Stuart Yates
dc.description.urihttp://www.elsevier.com/wps/find/journaldescription.cws_home/622879/description#description
dc.identifier.citationJournal of Functional Analysis, 2002; 188(1):111-136
dc.identifier.doi10.1006/jfan.2001.3841
dc.identifier.issn0022-1236
dc.identifier.orcidVarghese, M. [0000-0002-1100-3595]
dc.identifier.urihttp://hdl.handle.net/2440/3596
dc.language.isoen
dc.publisherAcademic Press Inc
dc.source.urihttps://doi.org/10.1006/jfan.2001.3841
dc.subjectHarper operator
dc.subjectapproximation theorems
dc.subjectamenable groups
dc.subjectvon Neumann algebras
dc.subjectgraphs
dc.subjectFuglede–Kadison determinant
dc.subjectalgebraic number theory
dc.titleApproximating spectral invariants of Harper operators on graphs
dc.typeJournal article
pubs.publication-statusPublished

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