Journal
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
Volume 51, Issue -, Pages 545-564Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0013091505001616
Keywords
Colombeau algebra; generalized manifold; generalized function; differential calculus; trace; support
Categories
Ask authors/readers for more resources
We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available