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© 2018

Distributions, Partial Differential Equations, and Harmonic Analysis

  • 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

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Dorina Mitrea
    Pages 1-16
  3. Dorina Mitrea
    Pages 117-202
  4. Dorina Mitrea
    Pages 203-214
  5. Dorina Mitrea
    Pages 215-231
  6. Dorina Mitrea
    Pages 233-320
  7. Dorina Mitrea
    Pages 321-332
  8. Dorina Mitrea
    Pages 333-353
  9. Dorina Mitrea
    Pages 355-386
  10. Dorina Mitrea
    Pages 387-424
  11. Dorina Mitrea
    Pages 425-496
  12. Dorina Mitrea
    Pages 497-541
  13. Dorina Mitrea
    Pages 543-590
  14. Back Matter
    Pages 591-600

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.

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). 

Keywords

Distributions Fourier Analysis Fundamental Solutions Partial Diffential Equations texbook Potential Theory Laplacian Helmholtz operator Cauchy-Reimann operator Dirac Operator

Authors and affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

About the authors

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

Bibliographic information

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