Distributions, Partial Differential Equations, and Harmonic Analysis: (Universitext)

​The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.​

Table of Contents:
​Introduction.- Summary of Topological and Functional Analysis Results.- Weak Derivatives.- The Space D0() of Distributions.- The Fourier Transform.- The Space of Tempered Distributions.- Fundamental Solution.- The Laplace Operator.- The Heat Operator.- The Wave Operator.- The Lame Operator.- Fundamental Solutions for Other Operators.- Hypoelliptic operators.- Sobolev spaces.- Appendix.- References. ​

About the Author :
Dorina Mitrea is a Professor at University of Missouri in the Mathematics Department.

Review :
“The book is very carefully written and its emphasis on applications in partial differential equations does justice to the nature and importance of the theory of distributions in modern analysis. An attractive feature of this work is the large number of exercises including solutions, both interspersed in the text and following each chapter. It is an ideal starting point to delve into the theory of distributions.” (M. Kunzinger, Monatshefte für Mathematik, 2015) “The monograph under consideration aims at a thorough introduction to ideas and techniques of distribution theory with application to partial differential equations. … the first part of this book is an excellent and carefully written introduction to the ideas and first applications of distribution theory which can be recommended for self-study for graduate students, while the second part contains a great variety of explicit formulas for tempered fundamental solutions interesting for the specialists in that area.” (Michael Langenbruch, zbMATH 1308.46002, 2015) “The book under review deals with the distribution theory and its applications to partial differential equations. … proofs are extremely detailed for the benefit of beginners, and there are a large number of exercises, more than half of which are accompanied by solutions. … one appreciates the author’s remarkable effort to present the subject in a form as clear and accessible as possible … . This makes this textbook ideal for upper undergraduate to graduate level courses on the subject.” (Fabio Nicola, Mathematical Reviews, September, 2014)