Mathematics – Functional Analysis
Scientific paper
2010-03-17
Mathematics
Functional Analysis
19 pages
Scientific paper
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 $M$.
Dave Shantanu
Hoermann Guenther
Kunzinger Michael
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