A General Dixmier Trace Formula for the Density of States on Open Manifolds - Hekkelman, Eva-Maria; McDonald, Edward (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
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.