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...
Published in: | Proceedings of the American Mathematical Society |
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ftsubgoettingen:oai:publications.goettingen-research-online.de:2/4479 2023-12-10T09:48:10+01:00 Approximating spectral invariants of Harper operators on graphs II Mathai, Varghese Schick, Thomas Yates, Stuart Mathai, Varghese Schick, Thomas Yates, Stuart 2003 https://resolver.sub.uni-goettingen.de/purl?gro-2/4479 https://doi.org/10.1090/S0002-9939-02-06739-4 en eng https://resolver.sub.uni-goettingen.de/purl?gro-2/4479 doi:10.1090/S0002-9939-02-06739-4 3146687 info:eu-repo/semantics/openAccess info:eu-repo/semantics/article journal_article no yes 2003 ftsubgoettingen https://doi.org/10.1090/S0002-9939-02-06739-4 2023-11-12T23:11:54Z 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 speed. Article in Journal/Newspaper DML GRO.publications (Göttingen Research Online Publications - Göttingen University) Harper ENVELOPE(-57.050,-57.050,-84.050,-84.050) Proceedings of the American Mathematical Society 131 6 1917 1923 |
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Open Polar |
collection |
GRO.publications (Göttingen Research Online Publications - Göttingen University) |
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ftsubgoettingen |
language |
English |
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 speed. |
author2 |
Mathai, Varghese Schick, Thomas Yates, Stuart |
format |
Article in Journal/Newspaper |
author |
Mathai, Varghese Schick, Thomas Yates, Stuart |
spellingShingle |
Mathai, Varghese Schick, Thomas Yates, Stuart Approximating spectral invariants of Harper operators on graphs II |
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 |
publishDate |
2003 |
url |
https://resolver.sub.uni-goettingen.de/purl?gro-2/4479 https://doi.org/10.1090/S0002-9939-02-06739-4 |
long_lat |
ENVELOPE(-57.050,-57.050,-84.050,-84.050) |
geographic |
Harper |
geographic_facet |
Harper |
genre |
DML |
genre_facet |
DML |
op_relation |
https://resolver.sub.uni-goettingen.de/purl?gro-2/4479 doi:10.1090/S0002-9939-02-06739-4 3146687 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1090/S0002-9939-02-06739-4 |
container_title |
Proceedings of the American Mathematical Society |
container_volume |
131 |
container_issue |
6 |
container_start_page |
1917 |
op_container_end_page |
1923 |
_version_ |
1784892082419138560 |