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A global theory of algebras of generalized functions II: tensor distributions

A global theory of algebras of generalized functions II: tensor distributions
A global theory of algebras of generalized functions II: tensor distributions
We extend the construction of [19] 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.
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
139-199
Grosser, Michael
e3114c32-8575-4ecc-bfd5-5560e40bbf90
Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James
719cd73f-c462-417d-a341-0b042db88634
Grosser, Michael
e3114c32-8575-4ecc-bfd5-5560e40bbf90
Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James
719cd73f-c462-417d-a341-0b042db88634

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.

Record type: Article

Abstract

We extend the construction of [19] 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.

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Published date: 19 March 2012
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
Organisations: Mathematics

Identifiers

Local EPrints ID: 336198
URI: https://eprints.soton.ac.uk/id/eprint/336198
PURE UUID: c1c83890-8655-40ea-82c6-7aee42ed0cd9
ORCID for James Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 20 Mar 2012 14:55
Last modified: 17 Sep 2019 01:11

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