Distributions and Operators

  • Gerd Grubb

Part of the Graduate Texts in Mathematics book series (GTM, volume 252)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Distributions and derivatives

    1. Front Matter
      Pages 1-1
    2. Gerd Grubb
      Pages 3-7
    3. Gerd Grubb
      Pages 9-25
  3. Extensions and applications

    1. Front Matter
      Pages 55-55
    2. Gerd Grubb
      Pages 57-94
    3. Gerd Grubb
      Pages 95-122
  4. Pseudodifferential operators

    1. Front Matter
      Pages 161-161
  5. Boundary value problems

    1. Front Matter
      Pages 216-216
    2. Gerd Grubb
      Pages 251-304
  6. Topics on Hilbert space operators

    1. Front Matter
      Pages 335-335
    2. Gerd Grubb
      Pages 337-372
    3. Gerd Grubb
      Pages 373-404
    4. Gerd Grubb
      Pages 405-422

About this book

Introduction

This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. Additionally, the aim is to show how the theory is combined with the study of operators in Hilbert space by methods of functional analysis, with applications to partial and ordinary differential equations. Here, the author provides an introduction to unbounded operators in Hilbert space, including a complete theory of extensions of operators, and applications using contraction semigroups.

In more advanced parts of the book, the author shows how distribution theory is used to define pseudodifferential operators on manifolds, and gives a detailed introduction to the pseudodifferential boundary operator calculus initiated by Boutet de Monvel, which allows a modern treatment of elliptic boundary value problems.

 

This book is aimed at graduate students, as well as researchers interested in its special topics, and as such, the author provides careful explanations along with complete proofs, and a bibliography of relevant books and papers. Each chapter has been enhanced with many exercises and examples.

Unique topics include:

* the interplay between distribution theory and concrete operators;

* families of extensions of nonselfadjoint operators;

* an illustration of the solution maps between distribution spaces by a fully worked out constant-coefficient case;

* the pseudodifferential boundary operator calculus;

* the Calderón projector and its applications.

 

Gerd Grubb is Professor of Mathematics at University of Copenhagen.

Keywords

Boundary value problem Derivative Hilbert space Sobolev space calculus differential equation distribution functional analysis partial differential equation

Authors and affiliations

  • Gerd Grubb
    • 1
  1. 1.Department of Mathematical SciencesUniversity of CopenhagenDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-84895-2
  • Copyright Information Springer New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-84894-5
  • Online ISBN 978-0-387-84895-2
  • Series Print ISSN 0072-5285
  • About this book