On Traces of Operators Associated with Actions of Compact Lie Groups

Given a pair (M,X), where X is a smooth submanifold in a closed smooth manifold M, we study the operation that takes each operator D on the ambient manifold to a certain operator on the submanifold. The latter operator is called the trace of D. More precisely, we study traces of operators associated with actions of compact Lie groups on M. We show that traces of such operators are localized at special submanifolds in X and study the structure of the traces on these submanifolds. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.