Approximating Spectral invariants of Harper operators on graphs II

We 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. The spectral density function of the DML is defined using the von Neumann trace associated with the free action of a discrete group on a graph...

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Main Authors: Mathai, Varghese, Schick, Thomas, Yates, Stuart
Format: Text
Language:unknown
Published: arXiv 2002
Subjects:
Spectral Theory math.SP
FOS Mathematics
58G25Primary 39A12 Secondary
Harper
DML
Online Access:https://dx.doi.org/10.48550/arxiv.math/0201127
https://arxiv.org/abs/math/0201127
id ftdatacite:10.48550/arxiv.math/0201127
record_format openpolar
spelling ftdatacite:10.48550/arxiv.math/0201127 2023-05-15T16:01:17+02:00 Approximating Spectral invariants of Harper operators on graphs II Mathai, Varghese Schick, Thomas Yates, Stuart 2002 https://dx.doi.org/10.48550/arxiv.math/0201127 https://arxiv.org/abs/math/0201127 unknown arXiv https://dx.doi.org/10.1090/s0002-9939-02-06739-4 Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ Spectral Theory math.SP FOS Mathematics 58G25Primary 39A12 Secondary article-journal Article ScholarlyArticle Text 2002 ftdatacite https://doi.org/10.48550/arxiv.math/0201127 https://doi.org/10.1090/s0002-9939-02-06739-4 2022-04-01T16:42:12Z We 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. The spectral density function of the DML is defined using the von Neumann trace associated with the free action of a discrete group on a graph. The main result in this paper states that when the group is amenable, the spectral density function is equal to the integrated density of states of the DML that is defined using either Dirichlet or Neumann boundary conditions. This establishes the main conjecture in a paper by Mathai and Yates. The result is generalized to other self adjoint operators with finite propagation. : LaTeX2e, 7 pages Text DML DataCite Metadata Store (German National Library of Science and Technology) Harper ENVELOPE(-57.050,-57.050,-84.050,-84.050)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Spectral Theory math.SP
FOS Mathematics
58G25Primary 39A12 Secondary
spellingShingle Spectral Theory math.SP
FOS Mathematics
58G25Primary 39A12 Secondary
Mathai, Varghese
Schick, Thomas
Yates, Stuart
Approximating Spectral invariants of Harper operators on graphs II
topic_facet Spectral Theory math.SP
FOS Mathematics
58G25Primary 39A12 Secondary
description We 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. The spectral density function of the DML is defined using the von Neumann trace associated with the free action of a discrete group on a graph. The main result in this paper states that when the group is amenable, the spectral density function is equal to the integrated density of states of the DML that is defined using either Dirichlet or Neumann boundary conditions. This establishes the main conjecture in a paper by Mathai and Yates. The result is generalized to other self adjoint operators with finite propagation. : LaTeX2e, 7 pages
format Text
author Mathai, Varghese
Schick, Thomas
Yates, Stuart
author_facet Mathai, Varghese
Schick, Thomas
Yates, Stuart
author_sort Mathai, Varghese
title Approximating Spectral invariants of Harper operators on graphs II
title_short Approximating Spectral invariants of Harper operators on graphs II
title_full Approximating Spectral invariants of Harper operators on graphs II
title_fullStr Approximating Spectral invariants of Harper operators on graphs II
title_full_unstemmed Approximating Spectral invariants of Harper operators on graphs II
title_sort approximating spectral invariants of harper operators on graphs ii
publisher arXiv
publishDate 2002
url https://dx.doi.org/10.48550/arxiv.math/0201127
https://arxiv.org/abs/math/0201127
long_lat ENVELOPE(-57.050,-57.050,-84.050,-84.050)
geographic Harper
geographic_facet Harper
genre DML
genre_facet DML
op_relation https://dx.doi.org/10.1090/s0002-9939-02-06739-4
op_rights Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004
http://arxiv.org/licenses/assumed-1991-2003/
op_doi https://doi.org/10.48550/arxiv.math/0201127
https://doi.org/10.1090/s0002-9939-02-06739-4
_version_ 1766397216002408448

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