We present a geometric approach to defining an algebra G Λ(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space DOE(M) of distributions on M. Based on differential calculus in convenient vector spaces we achieve an intrinsic construction of G Λ(M). G Λ(M) i
Geometrical embeddings of distributions into algebras of generalized functions
β Scribed by Shantanu Dave
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 153 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
We use spectral theory to produce embeddings of distributions into algebras of generalized functions on a closed (compact without boundary) Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the distributions (Β© 2010 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
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