Distributions
About this book
This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encompasses the Banach and Fréchet spaces and the same "weak" spaces. Alongside the usual operations – derivation, product, variable change, variable separation, restriction, extension and regularization – Distributions presents a new operation: weighting. This operation produces properties similar to those of convolution for distributions defined in any open space. Emphasis is placed on the extraction of convergent sub-sequences, the existence and study of primitives and the representation by gradient or by derivatives of continuous functions. Constructive methods are used to make these tools accessible to students and engineers.
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Information
Table of contents
- Cover
- Half-Title Page
- Title Page
- Copyright Page
- Contents
- Introduction
- Notations
- Chapter 1. Semi-Normed Spaces and Function Spaces
- Chapter 2. Space of Test Functions
- Chapter 3. Space of Distributions
- Chapter 4. Extraction of Convergent Subsequences
- Chapter 5. Operations on Distributions
- Chapter 6. Restriction, Gluing and Support
- Chapter 7. Weighting
- Chapter 8. Regularization and Applications
- Chapter 9. Potentials and Singular Functions
- Chapter 10. Line Integral of a Continuous Field
- Chapter 11. Primitives of Functions
- Chapter 12. Properties of Primitives of Distributions
- Chapter 13. Existence of Primitives
- Chapter 14. Distributions of Distributions
- Chapter 15. Separation of Variables
- Chapter 16. Banach Space Valued Distributions
- Appendix
- Bibliography
- Index
- Other titles from iSTE in Mathematics and Statistics
- EULA
