文档介绍：Harmonic Function
Theory
Second Edition
Sheldon Axler Paul Bourdon Wade Ramey
26 December 2000
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©2001 Springer-Verlag New York, Inc.
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Contents
Preface ix
Acknowledgments xi
Chapter 1
Basic Properties of Harmonic Functions 1
Definitions and Examples ....................... 1
Invariance Properties .......................... 2
The Mean-Value Property ........................ 4
The Maximum Principle ......................... 7
The Poisson Kernel for the Ball .................... 9
The Dirichlet Problem for the Ball .................. 12
Converse of the Mean-Value Property ................ 17
Real Analyticity and Homogeneous Expansions .......... 19
Origin of the Term “Harmonic”.................... 25
Exercises .......................