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

Published 26 Apr 2023 in math-ph, cond-mat.other, math.FA, math.MG, math.MP, and math.SP | (2304.13272v2)

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.

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