Geometric Theory of Generalized Functions with Applications to General Relativity / Edition 1

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Overview

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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Product Details

  • ISBN-13: 9789048158805
  • Publisher: Springer Netherlands
  • Publication date: 12/7/2010
  • Series: Mathematics and Its Applications (closed) Series , #537
  • Edition description: Softcover reprint of the original 1st ed. 2001
  • Edition number: 1
  • Pages: 505
  • Product dimensions: 6.00 (w) x 9.00 (h) x 1.20 (d)

Table of Contents

Preface. Acknowledgments. Introduction. 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.

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