Geometric Theory of Generalized Functions with Applications to General Relativity
By: by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer
Contributors: Kunzinger, Michael; Oberguggenberger, Michael; Steinbauer, Roland
Series: Mathematics and Its Applications -- 537; Mathematics and Its Applications -- 537
Publisher: Springer Netherlands
Published: 2001
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 505
ISBN-13: 9789048158805; 9789401598453
Subjects: Functional analysis; Mathematics; Topological Groups; Global analysis
Description: 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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