Overview
- Largely self-contained, rapid introduction to the theory of distributions and its applications to partial differential equations
- Contains the computation of fundamental solutions for the Laplacian, heat, wave, Lam\'e, Schrodinger, and Cauchy operators
- Each chapter contains exercises and many have solutions at the end of the book
Part of the book series: Universitext (UTX)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
“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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Distributions, Partial Differential Equations, and Harmonic Analysis
Authors: Dorina Mitrea
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-8208-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
eBook ISBN: 978-1-4614-8208-6Published: 20 September 2013
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XXI, 460
Topics: Partial Differential Equations, Functional Analysis, Fourier Analysis, Potential Theory