Eva-Maria Hekkelman, Edward McDonald, “A General Dixmier Trace Formula for the Density of States on Open Manifolds”, SIGMA, 2024, том 20,007, 34 стр.

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

Eva-Maria Hekkelman^a, Edward McDonald^b

^a School of Mathematics and Statistics, University of New South Wales, Kensington, NSW 2052, Australia
^b Department of Mathematics, Penn State University, University Park, PA 16802, USA

Аннотация: 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.

Ключевые слова: density of states, index theory, Dixmier trace, singular trace, bounded geometry, manifolds.

MSC: 47N50, 58J42, 53C23

Поступила: 27 апреля 2023 г.; в окончательном варианте 10 января 2024 г.; опубликована 17 января 2024 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2024.007