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Distributions : theory and applications

Author: J J Duistermaat; Johan A C Kolk
Publisher: [S.l.] : Birkhäuser ; New York : Springer, ©2010.
Series: Cornerstones (Birkhäuser Verlag)
Edition/Format:   eBook : Document : 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. Throughout the book, methods are developed to deal with  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Duistermaat, J. J.
Distributions.
New York : Birkhäuser, 2010
(DLC) 2010932757
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J J Duistermaat; Johan A C Kolk
ISBN: 9780817646752 0817646752
OCLC Number: 668096001
Description: 1 online resource (xvi, 445 p.)
Contents: Preface --
Motivation --
Test Functions --
Distributions --
Differentiation of Distributions --
Convergence of Distributions --
Taylor Expansion in Several Variables --
Localization --
Distributions with Compact Support --
Multiplication by Functions --
Transposition, Pullback and Push forward --
Convolution of Distributions --
Fundamental Solutions --
Fractional Integration and Differentiation --
Fourier Transformation --
Fourier Series --
Fundamental Solutions and Fourier Transformation --
Supports and Fourier Transformation --
Sobolev Spaces --
Appendix: Results from Measure Theory in the Context of Distributions --
Examination Exercises with Solutions --
Solutions to Selected Exercises --
References --
Index.
Series Title: Cornerstones (Birkhäuser Verlag)
Responsibility: J.J. Duistermaat, J.A.C. Kolk ; translated from the 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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