 

Michael Grosser, Michael Kunzinger, Roland Steinbauer, and James A. Vickers
A global theory of algebras of generalized functions. II. Tensor distributions view print


Published: 
March 19, 2012 
Keywords: 
Tensor distributions, algebras of generalized functions, generalized tensor fields, Schwartz impossibility result, diffeomorphism invariant Colombeau algebras, calculus in convenient vector spaces 
Subject: 
Primary 46F30; Secondary 46T30, 26E15, 58B10, 46A17 


Abstract
We extend the construction of the authors' paper of 2002 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.


Acknowledgements
The first author was supported by FWF grants P23714, Y237 and P20525 of the Austrian Science Fund


Author information
Michael Grosser:
University of Vienna, Faculty of Mathematics
michael.grosser@univie.ac.at
Michael Kunzinger:
University of Vienna, Faculty of Mathematics
michael.kunzinger@univie.ac.at
Roland Steinbauer:
University of Vienna, Faculty of Mathematics
roland.steinbauer@univie.ac.at
James A. Vickers:
School of Mathematics, University of Southampton
J.A.Vickers@maths.soton.ac.uk

