Distribution Theory: Convolution, Fourier Transform, and Laplace Transform

Gerrit van Dijk

Published by De Gruyter 2013

Distribution Theory

Convolution, Fourier Transform, and Laplace Transform

Gerrit van Dijk

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110298512

Overview
Contents

About this book

The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added.

It is suitable for a one-semester course at the advanced undergraduate or beginning graduate level or for self-study.

Every chapter starts with a summary and learning targets
Includes many excercises
Cocise and well-structured introduction to the topic

Author / Editor information

Gerrit van Dijk, Leiden University, The Netherlands.

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	vii
1 Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2 Definition and First Properties of Distributions Requires Authentication Unlicensed Licensed Download PDF	3
3 Differentiating Distributions Requires Authentication Unlicensed Licensed Download PDF	9
4 Multiplication and Convergence of Distributions Requires Authentication Unlicensed Licensed Download PDF	22
5 Distributions with Compact Support Requires Authentication Unlicensed Licensed Download PDF	26
6 Convolution of Distributions Requires Authentication Unlicensed Licensed Download PDF	31
7 The Fourier Transform Requires Authentication Unlicensed Licensed Download PDF	52
8 The Laplace Transform Requires Authentication Unlicensed Licensed Download PDF	74
9 Summable Distributions Requires Authentication Unlicensed Licensed Download PDF	82
10 Appendix Requires Authentication Unlicensed Licensed Download PDF	90
11 Hints to the Exercises Requires Authentication Unlicensed Licensed Download PDF	102
References Requires Authentication Unlicensed Licensed Download PDF	107
Index Requires Authentication Unlicensed Licensed Download PDF	109
Backmatter Requires Authentication Unlicensed Licensed Download PDF	111

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Students of Mathematics, lecturers on analysis and differential equations, academic libraries.
Pages
- Front matter: 8
- Main content: 109
Illustrations
- Illustrations: 1
Keywords: Distribution Theory; Fourier Transform; Laplace Transform; Tempered Distribution; Heat Equation

eBook

Published: March 22, 2013
ISBN: 9783110298512

Hardcover

Published: March 15, 2013
ISBN: 9783110295917