Distributions
Subtitle: theory and applications
By: J.J. Duistermaat, J.A.C. Kolk ; translated from Dutch by J.P. van Braam Houckgeest
Contributors: Kolk, Johan A. C., 1947-; Braam Houckgeest, J. P. van
Series: Cornerstones; Cornerstones (Birkhäuser Verlag)
Publisher: Birkhäuser
Published: 2010
Place of publication: New York
Language: eng
Number of pages: 445
ISBN-13: 9780817646721
Subjects: Fourier transformations; Theory of distributions (Functional analysis)
Description: "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.
Notes: Includes bibliographical references and index.
Table of contents: title: 1. Motivation; title: 2. Test functions; title: 3. Distributions; title: 4. Differentiation of distributions; title: 5. Convergence of distributions; title: 6. Taylor expansion in several variables; title: 7. Localization; title: 8. Distributions with compact support; title: 9. Multiplication by functions; title: 10. Transposition: pullback and pushforward; title: 11. Convolution of distributions; title: 12. Fundamental solutions; title: 13. Fractional integration and differentiation; title: 13.1. The case of dimension one; title: 13.2. Wave family; title: 13.3. Appendix: Euler's gamma function; title: 14. Fourier transform; title: 15. Distribution kernels; title: 16. Fourier series; title: 17. Fundamental solutions and Fourier Transform; title: 18. Supports and Fourier Transform; title: 19. Sobolev spaces; title: 20. Appendix: Integration; title: 21. Solutions to selected problems.