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-xi
  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 45-57
  5. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 59-72
  6. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 73-109
  7. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 111-142
  8. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 143-169
  9. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 171-190
  10. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 191-207
  11. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 209-221
  12. Sheldon Axler, Paul Bourdon, Wade Ramey
    Pages 223-238
  13. Back Matter
    Pages 239-263

About this book

Introduction

This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.

Keywords

Harmonic Function Theory Harmonic Functions Complex analysis integral integration Poisson integral

Authors and affiliations

  • Sheldon Axler
    • 1
  • Paul Bourdon
    • 2
  • Wade Ramey
    • 3
  1. 1.Mathematics DepartmentSan Francisco State UniversitySan FranciscoUSA
  2. 2.Mathematics DepartmentWashington and Lee UniversityLexingtonUSA
  3. 3.BerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-8137-3
  • Copyright Information Springer Science+Business Media New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2911-2
  • Online ISBN 978-1-4757-8137-3
  • Series Print ISSN 0072-5285
  • About this book