Universitext

Distributions, Partial Differential Equations, and Harmonic Analysis

Authors: Mitrea, Dorina

  • ​ ​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
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eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-8208-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4614-8207-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
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About this Textbook

​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.​

About the authors

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

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)


Table of contents (13 chapters)

  • Weak Derivatives

    Mitrea, Dorina

    Pages 1-16

  • The Space $$\mathcal{D}^{\prime}(\Omega )$$ of Distributions

    Mitrea, Dorina

    Pages 17-87

  • The Schwartz Space and the Fourier Transform

    Mitrea, Dorina

    Pages 89-108

  • The Space of Tempered Distributions

    Mitrea, Dorina

    Pages 109-187

  • The Concept of a Fundamental Solution

    Mitrea, Dorina

    Pages 189-200

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-8208-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4614-8207-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Distributions, Partial Differential Equations, and Harmonic Analysis
Authors
Series Title
Universitext
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-8208-6
DOI
10.1007/978-1-4614-8208-6
Softcover ISBN
978-1-4614-8207-9
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XXI, 460
Topics