Ait Ben H. The Theory of Distributions. Introduction 2023

Textbook in PDF format

Many physical, chemical, biological and even economic phenomena can be modeled by differential or partial differential equations, and the framework of distribution theory is the most efficient way to study these equations. A solid familiarity with the language of distributions has become almost indispensable in order to treat these questions efficiently. This book presents the theory of distributions in as clear a sense as possible while providing the reader with a background containing the essential and most important results on distributions. Together with a thorough grounding, it also provides a series of exercises and detailed solutions. The Theory of Distributions is intended for master’s students in mathematics and for students preparing for the agrégation certification in mathematics or those studying the physical sciences or engineering.
Preface.
Introduction.
Topological Vector Spaces.
Spaces of Test Functions.
Distributions on an Open Set of Rd.
Operations on Distributions.
Distribution Support.
Convolution of Distributions.
Schwartz Spaces and Tempered Distributions.
Fourier Transform.
Applications to ODEs and PDEs.
Appendix.
References.
Index