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 book, 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.
Author(s): Svetlin G. Georgiev (auth.)
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: VIII, 218
Tags: Functional Analysis; Ordinary Differential Equations; Partial Differential Equations; Fourier Analysis
Front Matter....Pages i-viii
Introduction....Pages 1-25
Generalities on Distributions....Pages 27-63
Differentiation....Pages 65-85
Homogeneous Distributions....Pages 87-97
Direct Product of Distributions....Pages 99-107
Convolutions....Pages 109-149
Tempered Distributions....Pages 151-159
Integral Transforms....Pages 161-177
Fundamental Solutions....Pages 179-185
Sobolev Spaces....Pages 187-213
Back Matter....Pages 215-218
