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 |
| Published: |
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| Summary: | 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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| ISSN: | 1815-0659 |