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Harmonic Function Theory

  • Sheldon Axler
  • Paul Bourdon
  • Wade Ramey

Part of the Graduate Texts in Mathematics book series (GTM, volume 137)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 1-29
  3. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 31-44
  4. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 45-58
  5. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 59-71
  6. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 73-96
  7. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 97-124
  8. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 125-149
  9. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 151-168
  10. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 169-182
  11. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 183-195
  12. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 197-212
  13. Back Matter
    Pages 213-233

About this book

Introduction

Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.

Keywords

Harmonic Function Theory Harmonic Functions Laplace's equation complex analysis functional analysis harmonic analysis integral

Authors and affiliations

  • Sheldon Axler
    • 1
  • Paul Bourdon
    • 2
  • Wade Ramey
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsWashington and Lee UniversityLexingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97238
  • Copyright Information Springer Science+Business Media New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-1186-5
  • Online ISBN 978-0-387-21527-3
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site