Generalized Functions and Partial Differential Equations (Dover Books on Mathematics)

Book Details

• Author: Avner Friedman

• Brand: Dover

• Edition: Illustrated

• Binding: Paperback

• Number of Pages: 352

• Release Date: 10-12-2005

• ISBN: 9780486446103

• Package Dimensions: 8.4 x 5.4 x 0.8 inches

• Languages: English

About the Book

"Generalized Functions and Distributions" by Avner Friedman is a comprehensive and self-contained text that introduces the theory of generalized functions and distributions, while exploring their wide applications in solving partial differential equations. This book is based on the influential works of L. Schwartz, who pioneered the theory of distributions, and Gelfand and Shilov, who expanded on generalized functions and their utility in tackling complex problems, including the Cauchy problem.

Friedman’s approach to generalized functions and distributions provides clarity and depth, making this book essential for anyone studying functional analysis and partial differential equations. The illustrated edition enriches the learning experience by visually representing the abstract concepts discussed in the text.

The book is specifically tailored for upper-level undergraduates and graduate students, with a background in both real and complex variables. While functional analysis (especially normed spaces) is helpful, it is not a prerequisite, as the author begins with an introductory chapter covering the necessary topological space background.

Key Features:

• In-depth coverage of the theory of generalized functions and distributions

• Applications to solving partial differential equations, with a focus on problems like the Cauchy problem and Goursat problem

• Treatment of fundamental solutions and the existence and differentiality of solutions

• Written for upper-level undergraduates and graduate students, assuming a solid background in real and complex variables

• Illustrated edition to enhance understanding of abstract mathematical concepts

• Supplementary materials including end-of-chapter problems, bibliographical remarks, and a bibliography for further research

This book is an invaluable resource for anyone seeking a clear and rigorous introduction to the theory and applications of generalized functions and distributions in the context of partial differential equations.