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Theory of Distributions

  • Textbook
  • © 2021

Overview

Authors:
  1. Svetlin G. Georgiev

    1. Department of Differential Equations Faculty of Mathematics and Informatics, University of Sofia “St. Kliment Ohridski”, Sofia, Bulgaria

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  • Helps the reader to understand theory of distributions help students with many examples
  • Solved problems problems with hints and problems with examples
  • Detailed proofs of the basic facts

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Svetlin G. Georgiev
    Pages 1-76

  3. Generalities on Distributions

    • Svetlin G. Georgiev
    Pages 77-112

  4. Differentiation

    • Svetlin G. Georgiev
    Pages 113-142

  5. Homogeneous Distributions

    • Svetlin G. Georgiev
    Pages 143-154

  6. The Direct Product of Distributions

    • Svetlin G. Georgiev
    Pages 155-164

  7. Convolutions

    • Svetlin G. Georgiev
    Pages 165-194

  8. Tempered Distributions

    • Svetlin G. Georgiev
    Pages 195-203

  9. Integral Transforms

    • Svetlin G. Georgiev
    Pages 205-218

  10. Fundamental Solutions

    • Svetlin G. Georgiev
    Pages 219-230

  11. Sobolev Spaces

    • Svetlin G. Georgiev
    Pages 231-258

  12. Back Matter

    Pages 259-262
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Keywords

About this book

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This second edition, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

Authors and Affiliations

  • Department of Differential Equations Faculty of Mathematics and Informatics, University of Sofia “St. Kliment Ohridski”, Sofia, Bulgaria

    Svetlin G. Georgiev

About the author

Svetlin G. Georgiev (born 1974, Bulgaria) has worked in various areas of mathematics. His current focus: harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales.

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