Graduate Texts in Mathematics

Harmonic Function Theory

Authors: Axler, Sheldon, Bourdon, Paul, Wade, Ramey

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Hardcover $74.95
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  • ISBN 978-1-4419-2911-2
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About this Textbook

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.

Reviews

From the reviews of the second edition:

"There are several major changes in this second edition … . Many exercises have been added and several photographs of mathematicians related to harmonic functions are included. The book is a nice introduction to the fundamental notions of potential theory." (European Mathematical Society Newsletter, June, 2002)

"We warmly recommend this textbook to graduate students interested in Harmonic Function Theory and/or related areas. We are sure that the reader will be able to appreciate the lively and illuminating discussions in this book, and therefore, will certainly gain a better understanding of the subject." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 67, 2001)

"This is a new edition of a nice textbook … on harmonic functions in Euclidean spaces, suitable for a beginning graduate level course. … New exercises are added and numerous minor improvements throughout the text are made." (Alexander Yu. Rashkovsky, Zentralblatt MATH, Vol. 959, 2001)


Table of contents (11 chapters)

  • Basic Properties of Harmonic Functions

    Axler, Sheldon (et al.)

    Pages 1-29

  • Bounded Harmonic Functions

    Axler, Sheldon (et al.)

    Pages 31-44

  • Positive Harmonic Functions

    Axler, Sheldon (et al.)

    Pages 45-57

  • The Kelvin Transform

    Axler, Sheldon (et al.)

    Pages 59-72

  • Harmonic Polynomials

    Axler, Sheldon (et al.)

    Pages 73-109

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4757-8137-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-387-95218-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4419-2911-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Harmonic Function Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
137
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-8137-3
DOI
10.1007/978-1-4757-8137-3
Hardcover ISBN
978-0-387-95218-5
Softcover ISBN
978-1-4419-2911-2
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XII, 264
Topics