A General Dixmier Trace Formula for the Density of States on Open Manifolds

We give an abstract formulation of the Dixmier trace formula for the density of states. This recovers prior versions and allows us to provide a Dixmier trace formula for the density of states of second-order elliptic differential operators on manifolds of bounded geometry satisfying a certain geomet...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2024
Main Authors: Hekkelman, Eva-Maria, McDonald, Edward
Format: Article
Language:English
Published: Інститут математики НАН України 2024
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212116
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:A General Dixmier Trace Formula for the Density of States on Open Manifolds. Eva-Maria Hekkelman and Edward McDonald. SIGMA 20 (2024), 007, 34 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Hekkelman, Eva-Maria
McDonald, Edward
author_facet Hekkelman, Eva-Maria
McDonald, Edward
citation_txt A General Dixmier Trace Formula for the Density of States on Open Manifolds. Eva-Maria Hekkelman and Edward McDonald. SIGMA 20 (2024), 007, 34 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We give an abstract formulation of the Dixmier trace formula for the density of states. This recovers prior versions and allows us to provide a Dixmier trace formula for the density of states of second-order elliptic differential operators on manifolds of bounded geometry satisfying a certain geometric condition. This formula gives a new perspective on Roe's index on open manifolds.
first_indexed 2026-03-17T00:18:25Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-17T00:18:25Z
publishDate 2024
publisher Інститут математики НАН України
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spelling Hekkelman, Eva-Maria
McDonald, Edward
2026-01-28T13:57:52Z
2024
A General Dixmier Trace Formula for the Density of States on Open Manifolds. Eva-Maria Hekkelman and Edward McDonald. SIGMA 20 (2024), 007, 34 pages
1815-0659
2020 Mathematics Subject Classification: 47N50; 58J42; 53C23
arXiv:2304.13272
https://nasplib.isofts.kiev.ua/handle/123456789/212116
https://doi.org/10.3842/SIGMA.2024.007
We give an abstract formulation of the Dixmier trace formula for the density of states. This recovers prior versions and allows us to provide a Dixmier trace formula for the density of states of second-order elliptic differential operators on manifolds of bounded geometry satisfying a certain geometric condition. This formula gives a new perspective on Roe's index on open manifolds.
We are grateful to Fedor Sukochev for his support and encouragement, and to Teun van Nuland for a helpful discussion. We thank the anonymous referees for their comments, which helped improve the paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
A General Dixmier Trace Formula for the Density of States on Open Manifolds
Article
published earlier
spellingShingle A General Dixmier Trace Formula for the Density of States on Open Manifolds
Hekkelman, Eva-Maria
McDonald, Edward
title A General Dixmier Trace Formula for the Density of States on Open Manifolds
title_full A General Dixmier Trace Formula for the Density of States on Open Manifolds
title_fullStr A General Dixmier Trace Formula for the Density of States on Open Manifolds
title_full_unstemmed A General Dixmier Trace Formula for the Density of States on Open Manifolds
title_short A General Dixmier Trace Formula for the Density of States on Open Manifolds
title_sort general dixmier trace formula for the density of states on open manifolds
url https://nasplib.isofts.kiev.ua/handle/123456789/212116
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