Integral Operators in the Theory of Linear Partial Differential Equations

  • Stefan Bergman

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 23)

Table of contents

  1. Front Matter
    Pages I-X
  2. Stefan Bergman
    Pages 1-9
  3. Stefan Bergman
    Pages 38-63
  4. Stefan Bergman
    Pages 63-81
  5. Stefan Bergman
    Pages 81-105
  6. Back Matter
    Pages 132-147

About this book

Introduction

The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve­ lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo­ retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.

Keywords

Integral Operators differential equation equation partial differential equation

Authors and affiliations

  • Stefan Bergman
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-64985-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1961
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64987-5
  • Online ISBN 978-3-642-64985-1
  • Series Print ISSN 0071-1136
  • About this book