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Distributions : theory and applications

Author: J J Duistermaat; Johan A C Kolk; J P van Braam Houckgeest
Publisher: New York : Birkhäuser, ©2010.
Series: Cornerstones (Birkhäuser Verlag)
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J J Duistermaat; Johan A C Kolk; J P van Braam Houckgeest
ISBN: 9780817646721 0817646728
OCLC Number: 666252121
Description: xvi, 445 p. : ill. ; 25 cm.
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.
Series Title: Cornerstones (Birkhäuser Verlag)
Responsibility: J.J. Duistermaat, J.A.C. Kolk ; translated from Dutch by J.P. van Braam Houckgeest.
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Abstract:

This text offers an application-oriented introduction to the theory of distributions. It presents distributions as a natural method of analysis from a mathematical and physical point of view. The  Read more...

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From the reviews: "This is a fantastic book...Even in this enlightened age, the theory of distributions is a highly misunderstood and undervalued business...All of this notwithstanding, learning it Read more...

 
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