A General Dixmier Trace Formula for the Density of States on Open Manifolds
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Published:2024-01-17
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
,Hekkelman Eva-Maria,Mcdonald Edward,
Abstract
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)