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Universitext

Distributions, Partial Differential Equations, and Harmonic Analysis

Authors: Mitrea, Dorina

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  • Pursues the development of distribution theory simultaneously with relevant incursions into partial differential equations and harmonic analysis
  • Written in a concise, rigorous, and largely self-contained form with a balanced treatment of the topics involved
  • Equips readers to handle subsequent courses dealing with allied topics, including: Harmonic Analysis, Partial Differential Equations, Boundary Integral Methods, Sobolev Spaces, Pseudodifferential Operators
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eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-030-03296-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-030-03295-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.
The main additions to the current, second edition, pertain to fundamental solutions (through the inclusion of the Helmholtz operator, the perturbed Dirac operator, and their iterations) and the theory of Sobolev spaces (built systematically from the ground up, exploiting natural connections with the Fourier Analysis developed earlier in the monograph). 

About the authors

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

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-030-03296-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-030-03295-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Distributions, Partial Differential Equations, and Harmonic Analysis
Authors
Series Title
Universitext
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-03296-8
DOI
10.1007/978-3-030-03296-8
Softcover ISBN
978-3-030-03295-1
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XXIII, 600
Number of Illustrations
1 b/w illustrations
Topics