Journal
TOKYO JOURNAL OF MATHEMATICS
Volume 36, Issue 1, Pages 25-47Publisher
PUBLICATION COMMITTEE, TOKYO JOURNAL MATHEMATICS
DOI: 10.3836/tjm/1374497511
Keywords
Regularization of distributions; wave equation; microlocal regularity
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Funding
- FWF, Austrian Science Fund [P 20525-N13, Y237-N13]
- Austrian Science Fund (FWF) [P 24420, Y 237] Funding Source: researchfish
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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.
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