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On the foundations of nonlinear generalized functions I and II /
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...
| Call Number: | Libro Electrónico |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence, R.I. :
American Mathematical Society,
©2001.
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| Series: | Memoirs of the American Mathematical Society ;
no. 729. |
| Subjects: | |
| Online Access: | Texto completo |
Table of 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.