調和函數理論第2版（簡體書）

Harmonic functions--the solutions of Laplaces equation--play a crucial role in many areas of mathematics, physics, and engineering. But learning about them is not always easy. At times the authors have agreed with Lord Kelvin and Peter Tait, who wrote ([18], Preface) There can be but one opinion as to the beauty and utility of this analysis of Laplace; but the manner in which it has been hitherto presented has seemed repulsive to the ablest mathematicians, and difficult to ordinary mathematical students.

Preface
Acknowledgments
CHAPTER 1 Basic Properties of Harmonic Functions
Definitions and Examples
Invariance Properties
The Mean-Value Property
The Maximum Principle
The Poisson Kernel for the Ball
The Dirichlet Problem for the Ball
Converse of the Mean-Value Property
Real Analyticity and Homogeneous Expansions
Origin of the Term Harmonic
Exercises
CHAPTER 2 Bounded Harmonic Functions
Liouvfile‘s Theorem
Isolated Singularities
Cauchy‘s Estimates
Normal Families
Maximum Principles
Limits Along Rays
Bounded Harmonic Functions on the Ball
Exercises
CHPATER 3 Positive Harmonic Functions
CHPATER 4 The Kelvin Transform
CHPATER 5 Harmonic Polynomials
CHPATER 6 Harmonic Hardy Spaces
CHPATER 7 Harmonic Funtions on Half-Spaces
CHAPTER 8 Harmonic Bergaman Spaces
CHAPTER 9 The Decomposition Theorem
CHAPTER 10 Annular Regions
CHAPTER 11 The Dirichlet Problem and Boundary Behavior
APPENDIX A Volume,Surface Area,and Interation on Spheres
APPENDIX B Harmonic Function Theory and Mathematica
References
Symbol Index
Index