Description |
1 online resource (xi, 93 pages) : illustrations |
Series |
Memoirs of the American Mathematical Society, 1947-6221 ; v. 729 |
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Memoirs of the American Mathematical Society ; no. 729. 0065-9266
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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)
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Theory of distributions (Functional analysis)
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Form |
Electronic book
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Author |
Grosser, Michael
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LC no. |
2001032795 |
ISBN |
9781470403225 |
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1470403226 |
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