Distributions, Partial Differential Equations, and Harmonic Analysis / Universitext (PDF)
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The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis.
The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions.
Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide.
Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity.
- Autor: Dorina Mitrea
- 2013, 2013, 460 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 1461482089
- ISBN-13: 9781461482086
- Erscheinungsdatum: 20.09.2013
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- Größe: 4.46 MB
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“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)
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