Harmonic Function Theory

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Springer Science & Business Media, Jan 25, 2001 - Mathematics - 259 pages
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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 email-supplements the text for readers who wish to explore harmonic function theory on a computer.
 

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Contents

XPTER
3
PTER
7
itive Harmonic Functions
45
PTER 4
58
PTER 5
73
Explicit Bases of 3mR and 9mS
92
Exercises
106
The Hilbert Space I12 B
121
Positive Harmonic Functions on the Upper HalfSpace
157
PTER 8
170
The Reproducing Kernel of the Upper HalfSpace
185
Removable Sets for Bounded Harmonic Functions
201
The Residue Theorem 2 13
217
The Perron Construction
226
ENDIX
239
ex
255

monic Functions on HalfSpaces
143

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