Journal
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
Volume 61, Issue 4, Pages 961-994Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S001309151800010X
Keywords
Colombeau algebra; generalized function; full; special; sharp topology; point values; locality; sheaf property
Categories
Funding
- Austrian Science Fund (FWF) [P23714, P26859, P30233]
- Austrian Science Fund (FWF) [P26859] Funding Source: Austrian Science Fund (FWF)
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We introduce full diffeomorphism-invariant Colombeau algebras with added e-dependence in the basic space. This unites the full and special settings of the theory into one single framework. Using locality conditions we find the appropriate definition of point values in full Colombeau algebras and show that special generalized points suffice to characterize elements of full Colombeau algebras. Moreover, we specify sufficient conditions for the sheaf property to hold and give a definition of the sharp topology in this framework.
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