For purposes of this book, the term "distributions" has the following definition.
By `distributions" we understand the linear and continuous functionals on the space D of the functions that are of indefinite differentiability and that have compact support.
Therefore, the book can be considered one on function theory, with two main sections:
*) Functional theory of distributions *) Algebraic theory of distributions
Operations performed on the distributions include:
This book is a short, yet reasonably thorough development of the operations that can be performed on functions that satisfy the premise of the definition.
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Charles Ashbacher (CharlesAshbacher)
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In a simple but mathematically coherent manner, this text examines the basis of the distribution theories devised by Schwartz and by Mikusinki. Rigorous and concise, it surveys the functional theory of distributions as well as the algebraic theory. Easy generalizations offer applications to a wide variety of problems. 1962 edition.