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**About this book :- **
**Harmonic Function Theory (2E) ** written by
** Sheldon Axler, Paul Bourdon, Wade Ramey **

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. The main purpose of this text, then, is to make learning about harmonic functions easier. We start at the beginning of the subject, assuming only that our readers have a good foundation in real and complex analysis along with a knowledge of some basic results from functional analysis. The first fifteen chapters of [15], for example, provide sufficient preparation. In several cases authors simplify standard proofs. For example, authors replace the usual tedious calculations showing that the Kelvin transform of a harmonic function is harmonic with some straightforward observations that authors believe are more revealing. Another example is authors proof of Bôcher’s Theorem, which is more elementary than the classical proofs.

(Sheldon Axler)

**Book Detail :- **
** Title: ** Harmonic Function Theory
** Edition: ** 2nd
** Author(s): ** Sheldon Axler, Paul Bourdon, Wade Ramey
** Publisher: ** Springer
** Series: ** Graduate Texts in Mathematics 137
** Year: ** 2001
** Pages: ** 273
** Type: ** PDF
** Language: ** English
** ISBN: ** 0387952187,9780387952185,9780387215273
** Country: ** US

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**About Author :- **

Author ** Sheldon Axler ** was valedictorian of his high school in Miami, Florida. He received his AB from Princeton University with highest honors, followed by a PhD in Mathematics from the University of California at Berkeley. As a Moore Instructor at MIT, Axler received a university-wide teaching award.

Axler was then an assistant professor, associate professor, and professor in the Mathematics Department at Michigan State University, where he received the first J. Sutherland Frame Teaching Award and the Distinguished Faculty Award.

Axler received the Lester R. Ford Award for expository writing from the Mathematical Association of America in 1996. In addition to publishing numerous research papers, Axler is the author of five mathematics textbooks, ranging from freshman to graduate level. His book Linear Algebra Done Right has been adopted as a textbook at over 260 universities.

Axler has served as Editor-in-Chief of the Mathematical Intelligencer and as Associate Editor of the American Mathematical Monthly. He has been a member of the Council of the American Mathematical Society and a member of the Board of Trustees of the Mathematical Sciences Research Institute. Axler currently serves on the editorial board of Springer’s series Undergraduate Texts in Mathematics, Graduate Texts in Mathematics, and Universitext.

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**Book Contents :- **
**Harmonic Function Theory (2E) ** written by
** Sheldon Axler, Paul Bourdon, Wade Ramey **
cover the following topics.

1. Basic Properties of Harmonic Functions

2. Bounded Harmonic Functions

3. Positive Harmonic Functions

4. The Kelvin Transform

5. Harmonic Polynomials

6. Harmonic Hardy Spaces

7. Harmonic Functions on Half-Spaces

8. Harmonic Bergman Spaces

9. The Decomposition Theorem

10. Annular Regions

11. The Dirichlet Problem and Boundary Behavior

Appendix A Volume, Surface Area, and Integration on Spheres

Appendix B Harmonic Function Theory and Mathematica

References

Symbol Index

Index

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