A global theory of algebras of generalized functions II: tensor distributions
Grosser, Michael, Kunzinger, Michael, Steinbauer, Roland and Vickers, James (2012) A global theory of algebras of generalized functions II: tensor distributions. New York Journal of Mathematics, 18, 139-199.
This is the latest version of this item.
- Publishers print
We extend the construction of  by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical embedding of distributional tensor fields also commutes with the Lie derivative. This construction provides the basis for applications of algebras of generalized functions in nonlinear distributional geometry and, in particular, to the study of spacetimes of low differentiability in general relativity.
|Keywords:||tensor distributions, algebras of generalized functions, generalized tensor fields, schwartz impossibility result, diffeomorphism invariant colombeau algebras, calculus in convenient vector spaces msc 2000: primary 46F30, secondary 46T30, 26E15, 58B10, 46A17|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics
|Date Deposited:||20 Mar 2012 14:55|
|Last Modified:||26 Apr 2013 05:32|
|Contributors:||Grosser, Michael (Author)
Kunzinger, Michael (Author)
Steinbauer, Roland (Author)
Vickers, James (Author)
|Date:||19 March 2012|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
Available Versions of this Item
A global theory of algebras of generalized functions II: tensor distributions. (deposited 14 May 2010 09:24)
- A global theory of algebras of generalized functions II: tensor distributions. (deposited 20 Mar 2012 14:55) [Currently Displayed]
Actions (login required)