An edition of Distributions
(2010)
Distributions
theory and applications
by J. J. Duistermaat
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"This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background."--Source other than Library of Congress.
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Book Details
Table of Contents
1. Motivation
2. Test functions
3. Distributions
4. Differentiation of distributions
5. Convergence of distributions
6. Taylor expansion in several variables
7. Localization
8. Distributions with compact support
9. Multiplication by functions
10. Transposition: pullback and pushforward
11. Convolution of distributions
12. Fundamental solutions
13. Fractional integration and differentiation
13.1. The case of dimension one
13.2. Wave family
13.3. Appendix: Euler's gamma function
14. Fourier transform
15. Distribution kernels
16. Fourier series
17. Fundamental solutions and Fourier Transform
18. Supports and Fourier Transform
19. Sobolev spaces
20. Appendix: Integration
21. Solutions to selected problems.
Edition Notes
Includes bibliographical references and index.
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| October 4, 2021 | Edited by ImportBot | import existing book |
| June 29, 2019 | Edited by MARC Bot | import existing book |
| June 14, 2012 | Created by LC Bot | import new book |