Theory of Distributions

by Svetlin G. Georgiev

Overview

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This second edition, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

Product Details

ISBN-13:	9783319195278
Publisher:	Springer-Verlag New York, LLC
Publication date:	07/13/2015
Sold by:	Barnes & Noble
Format:	eBook
File size:	6 MB

About the Author

Svetlin G. Georgiev (born 1974, Bulgaria) has worked in various areas of mathematics. His current focus: harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales.

Table of Contents

1 Introduction.- 2 Generalities on distributions.- 3 Differentiation.- 4 Homogeneous distributions.- 5 Direct product of distributions.- 6 Convolutions.- 7 Tempered distributions.- 8 Integral transforms.- 9 Fundamental solutions.- 10 Sobolev spaces.

Editorial Reviews

Uniquely, this work by Georgiev (Univ. of Sofia, Bulgaria) reads stylistically like a brief, basic, but exotic calculus text, replete with concrete sample calculations. Many researchers found distributions quite alien when they made the scene 65 years ago, but with this book, today’s mathematics and physics undergraduate students may well come to regard them as quite routine. Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (10), June, 2016)

From the Publisher