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Distributions : theory and applications / J.J. Duistermaat, J.A.C. Kolk ; translated from Dutch by J.P. van Braam Houckgeest.

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Author/Creator:
Duistermaat, J. J. (Johannes Jisse), 1942-
Language:
English.
Publication date:
2010
Imprint:
New York : Birkhäuser, c2010.
Format:
  • Book
  • xvi, 445 p. : ill. ; 25 cm.
Bibliography:
Includes bibliographical references and index.
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.
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 solutions that guide the reader along a path requiring only a minimal mathematical background."--Publisher's description.
Contributor:
Kolk, Johan A. C., 1947-
Braam Houckgeest, J. P. van.
Series:
Cornerstones
Cornerstones (Birkhäuser Verlag)
Subjects:
ISBN:
9780817646721
0817646728

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