Distributions, Partial Differential Equations, and Harmonic Analysis

  • Dorina Mitrea

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Dorina Mitrea
    Pages 1-16
  3. Dorina Mitrea
    Pages 109-187
  4. Dorina Mitrea
    Pages 189-200
  5. Dorina Mitrea
    Pages 201-216
  6. Dorina Mitrea
    Pages 217-275
  7. Dorina Mitrea
    Pages 277-288
  8. Dorina Mitrea
    Pages 289-308
  9. Dorina Mitrea
    Pages 309-339
  10. Dorina Mitrea
    Pages 341-374
  11. Dorina Mitrea
    Pages 375-414
  12. Dorina Mitrea
    Pages 415-447
  13. Back Matter
    Pages 449-460

About this book

Introduction

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.

Keywords

Distributions Fourier Analysis Fundamental Solutions Partial Diffential Equations texbook Potential Theory

Authors and affiliations

  • Dorina Mitrea
    • 1
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8208-6
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8207-9
  • Online ISBN 978-1-4614-8208-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book