The Theory of Distributions

A Nontechnical Introduction
Erscheinungsjahr 2007
ISBN: 978-0-521-55890-7
Verlag: Cambridge University Press

Buch, Englisch, 160 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 254 g

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.

Autoren/Hrsg.

Richards, J. Ian

Youn, Heekyung K.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Preface; 1. Introduction; 2. The elements of distribution theory: Section 1. Basic Definitions and Facts; Section 2. Convolutions; 3. Examples of distributions; 4. Fourier transforms; 5. Tempered distributions; 6. Extension to higher dimensions; 7. A general definition of multiplication and convolution for distributions; Appendices; Bibliography; Index.