Optimal regularization processes on complete Riemannian manifolds

Shantanu Dave, Guenther Hoermann, Michael Kunzinger

Published 2010-03-17, updated 2012-10-10Version 2

We study regularizations of Schwartz distributions on a complete Riemannian manifold $M$. These approximations are based on families of smoothing operators obtained from the solution operator to the wave equation on $M$ derived from the metric Laplacian. The resulting global regularization processes are optimal in the sense that they preserve the microlocal structure of distributions, commute with isometries and provide sheaf embeddings into algebras of generalized functions on $M$.