Geometric Theory of Generalized Functions with Applications to General Relativity
Author:   M. Grosser ,  M. Kunzinger ,  Michael Oberguggenberger ,  R. Steinbauer
Publisher:   Springer-Verlag New York Inc.
Edition:   2001 ed.
Volume:   537
ISBN:  

9781402001451


Pages:   505
Publication Date:   30 November 2001
Format:   Hardback
Availability:   In Print   Availability explained
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Geometric Theory of Generalized Functions with Applications to General Relativity


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Overview

This work provides a comprehensive introduction to the non-linear 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 ""non-linear 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.

Full Product Details

Author:   M. Grosser ,  M. Kunzinger ,  Michael Oberguggenberger ,  R. Steinbauer
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2001 ed.
Volume:   537
Dimensions:   Width: 15.50cm , Height: 2.80cm , Length: 23.50cm
Weight:   2.010kg
ISBN:  

9781402001451


ISBN 10:   1402001452
Pages:   505
Publication Date:   30 November 2001
Audience:   College/higher education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of 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.

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