The Theory of Distributions: A Nontechnical Introduction

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CUP Archive, Sep 29, 1995 - Mathematics - 147 pages
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This book is a self-contained introduction to the theory of distributions, sometimes called generalized functions. Most books on this subject are either intuitive or else rigorous but technically demanding. Here, by concentrating on the essential results, the authors have introduced the subject in a way that will most appeal to non-specialists, yet is still mathematically correct. Topics covered include: the Dirac delta function, generalized functions, dipoles, quadrupoles, pseudofunctions and Fourier transforms. The self-contained treatment does not require any knowledge of functional analysis or topological vector spaces; even measure theory is not needed for most of the book. The book, which can be used either to accompany a course or for self-study, is liberally supplied with exercises. It will be a valuable introduction to the theory of distributions and their applications for students or professionals in statistics, physics, engineering and economics.
 

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Clear, readable style.

Contents

Three modes for the evaluation of functions
4
Outline of further developments
11
Convolutions
21
Convolution of distributions
29
Dipoles quadrupoles 2ipoles
35
Fourier transforms
42
Properties of the Fourier transform
50
Tempered distributions
58
Further examples Fourier series
85
Fourier transforms on R
91
Tempered distributions on
94
General distributions on W
101
Distributions depending on a parameter
107
Multiplication and convolution
120
The Fubini Theorem and related results
131
The Structure Theorem
137

Examples
67
Bochners Theorem
74

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