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.
Поступила:27 апреля 2023 г.; в окончательном варианте 10 января 2024 г.; опубликована 17 января 2024 г.
Образец цитирования:
Eva-Maria Hekkelman, Edward McDonald, “A General Dixmier Trace Formula for the Density of States on Open Manifolds”, SIGMA, 20 (2024), 007, 34 pp.
\RBibitem{HekMcd24}
\by Eva-Maria~Hekkelman, Edward~McDonald
\paper A General Dixmier Trace Formula for the Density of States on Open Manifolds
\jour SIGMA
\yr 2024
\vol 20
\papernumber 007
\totalpages 34
\mathnet{http://mi.mathnet.ru/sigma2009}
\crossref{https://doi.org/10.3842/SIGMA.2024.007}
Цитирование в формате AMSBIB
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