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 |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| 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| _version_ | 1862680981621702656 |
|---|---|
| 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.
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| first_indexed | 2026-03-17T00:18:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212116 |
| 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 |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT hekkelmanevamaria ageneraldixmiertraceformulaforthedensityofstatesonopenmanifolds AT mcdonaldedward ageneraldixmiertraceformulaforthedensityofstatesonopenmanifolds AT hekkelmanevamaria generaldixmiertraceformulaforthedensityofstatesonopenmanifolds AT mcdonaldedward generaldixmiertraceformulaforthedensityofstatesonopenmanifolds |