Distribution Theory

Convolution, Fourier Transform, and Laplace Transform

Gerrit Dijk

• Publisher: De Gruyter
• Year: 2013
• Print ISBN: 9783110295917
• eBook ISBN: 9783110298512
• Edition: 1
• Topic: Mathématiques
• Subtopic: Mathématiques appliquées

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.

Table of contents

• Preface
• 1 Introduction
• 2 Definition and First Properties of Distributions
• 3 Differentiating Distributions
• 4 Multiplication and Convergence of Distributions
• 5 Distributions with Compact Support
• 6 Convolution of Distributions
• 7 The Fourier Transform
• 8 The Laplace Transform
• 9 Summable Distributions*
• 10 Appendix
• 11 Hints to the Exercises
• References
• Index