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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First Sentence:
The theory of distributions, founded by S. L. Sobolev and L. Schwartz, shows great power and flexibility in its natural domain, the theory of linear partial differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
distributional geometry, generalized group action, distributional shadow, slowly increasing symmetry group, point value characterization, strict delta function, tempered generalized functions, distributional curvature, generalized vector field, impulsive gravitational waves, classical distribution theory, vector bundle chart, model delta function, distributional setting, induced covariant derivative, null ideal, diffeomorphism invariance, delta net, gravitational shock waves, fine sheaf, impulsive limit, geodesic deviation equation, impulsive waves, sheaf morphism, bundle charts Key Phrases - Capitalized Phrases (CAPs): (learn more)
Classification Results, Applying Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The theory of distributions, founded by S. L. Sobolev and L. Schwartz, shows great power and flexibility in its natural domain, the theory of linear partial differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
distributional geometry, generalized group action, distributional shadow, slowly increasing symmetry group, point value characterization, strict delta function, tempered generalized functions, distributional curvature, generalized vector field, impulsive gravitational waves, classical distribution theory, vector bundle chart, model delta function, distributional setting, induced covariant derivative, null ideal, diffeomorphism invariance, delta net, gravitational shock waves, fine sheaf, impulsive limit, geodesic deviation equation, impulsive waves, sheaf morphism, bundle charts Key Phrases - Capitalized Phrases (CAPs): (learn more)
Classification Results, Applying Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 34
books:
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- Nonlinear Theory of Generalized Functions (Chapman & Hall/CRC Research Notes in Mathematics Series) by Michael Oberguggenberger on 8 pages
- General Relativity by Robert M. Wald on page 419, and Back Matter
- General Relativity: Proceedings of the Forty Sixth Scottish Universities Summer School in Physics, Aberdeen, July 1995 (Scottish Graduate Series) by G.S Hall in Back Matter (1), and Back Matter (2)
- Sheaves on Manifolds: With a Short History "Les debuts de la theorie des faisceaux" by Christian Houzel (Grundlehren der mathematischen Wissenschaften) by Masaki Kashiwara in Back Matter
- The Convenient Setting of Global Analysis (Mathematical Surveys and Monographs) by Andreas Kriegl in Back Matter
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