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Title On the foundations of nonlinear generalized functions I and II / Michael Grosser [and others]
Published Providence, R.I. : American Mathematical Society, ©2001

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Description 1 online resource (xi, 93 pages) : illustrations
Series Memoirs of the American Mathematical Society, 1947-6221 ; v. 729
Memoirs of the American Mathematical Society ; no. 729. 0065-9266
Contents Part 1. On the foundations of nonlinear generalized functions I 1. Introduction 2. Notation and terminology 3. Scheme of construction 4. Calculus 5. C- and J-formalism 6. Calculus on $U_\epsilon (\Omega)$ 7. Construction of a diffeomorphism invariant Colombeau algebra 8. Sheaf properties 9. Separating the basic definition from testing 10. Characterization results 11. Differential equations Part 2. On the foundations of nonlinear generalized functions II 12. Introduction to Part 2 13. A simple condition equivalent to negligibility 14. Some more calculus 15. Non-injectivity of the canonical homomorphism from $\mathcal {G}̂d(\Omega)$ into $\mathcal {G}̂e(\Omega)$ 16. Classification of smooth Colombeau algebras between $\mathcal {G}̂d(\Omega)$ and $\mathcal {G}̂e(\Omega)$ 17. The algebra $\mathcal {G}̂2$; classification results 18. Concluding remarks
Summary Part 1. On the Foundations of Nonlinear Generalized Functions I: Introduction Notation and terminology Scheme of construction Calculus C- and J-formalism Calculus on $U_\varepsilon(\Omega)$ Construction of a diffeomorphism invariant Colombeau algebra Sheaf properties Separating the basic definition from testing Characterization results Differential equations Part 2. On the Foundations of Nonlinear Generalized Functions II: Introduction to Part 2 A simple condition equivalent to negligibility Some more calculus Non-injectivity of the canonical homomorphism from ${\mathcal G}̂d(\Omega)$ into ${\mathcal G}̂e(\Omega)$ Classification of smooth Colombeau algebras between ${\mathcal G}̂d(\Omega)$ and ${\mathcal G}̂e(\Omega)$ The algebra ${\mathcal G}̂2$; classification results Concluding remarks Acknowledgments Bibliography
Notes "September 2001, volume 153, number 729 (end of volume)."
Bibliography Includes bibliographical references (pages 92-93)
Notes Print version record
Subject Theory of distributions (Functional analysis)
Theory of distributions (Functional analysis)
Form Electronic book
Author Grosser, Michael
LC no. 2001032795
ISBN 9781470403225
1470403226