On the Foundations of Nonlinear Generalized Functions I and II.

Intro -- Contents -- Abstract -- Preface -- Part 1. On the Foundations of Nonlinear Generalized Functions I -- Chapter 1. Introduction -- Chapter 2. Notation and Terminology -- Chapter 3. Scheme of construction -- Chapter 4. Calculus -- Chapter 5. C- and J-formalism -- Chapter 6. Calculus on U[sub(ε)](Ω) -- Chapter 7. Construction of a diffeomorphism invariant Colombeau algebra -- 7.1. The basis for the definition of the algebra -- 7.2. The approach taken by J. Jelínek -- 7.3. Stability under differentiation -- 7.4. Diffeomorphism invariance -- Chapter 8. Sheaf properties -- Chapter 9. Separating the basic definition from testing -- Chapter 10. Characterization results -- Chapter 11. Differential Equations -- Part 2. On the Foundations of Nonlinear Generalized Functions II -- Chapter 12. Introduction to Part 2 -- Chapter 13. A simple condition equivalent to negligibility -- Chapter 14. Some more calculus -- Chapter 15. Non-injectivity of the canonical homomorphism from G[sup(d)](Ω) into G[sup(e)](Ω) -- 15.1. Proof of the estimates (15.4) -- 15.2. Proof of smoothness of P -- 15.3. Proof of moderateness of P -- 15.4. Proof of P ∉ N[sup(d)] -- 15.5. Proof of P ∈ N[sup(e)] -- Chapter 16. Classification of smooth Colombeau algebras between G[sup(d)](Ω) and G[sup(e)](Ω) -- 16.1. The development leading from G[sup(e)](Ω) to G[sup(d)](Ω) -- 16.2. Classification of test objects -- 16.3. Classification of full smooth Colombeau algebras -- Chapter 17. The algebra G[sup(2)] -- classification results -- Chapter 18. Concluding remarks -- Acknowledgments -- Bibliography.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.