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Geometric Theory of Generalized Functions with Applications to General Relativity

Author: Michael Grosser; M Kunzinger; Michael Oberguggenberger; Roland Steinbauer
Publisher: Dordrecht : Springer Netherlands, 2001.
Series: Mathematics and Its Applications, 537.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael Grosser; M Kunzinger; Michael Oberguggenberger; Roland Steinbauer
ISBN: 9789401598453 9401598452
OCLC Number: 851366106
Description: 1 online resource (xv, 505 pages).
Contents: 1. Colombeau's Theory of Generalized Functions --
2. Diffeomorphism Invariant Colombeau Theory --
3. Generalized Functions on Manifolds --
4. Applications to Lie Group Analysis of Differential Equations --
5. Applications to General Relativity --
Appendices --
The Chain Rule for Higher Differentials --
References --
Author Index --
Index of Notation.
Series Title: Mathematics and Its Applications, 537.
Responsibility: by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer.
More information:

Abstract:

This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.

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