《实定理的复证明》是对Hadamard的格言“实域中两个真理之间的最好和最短路程是通过复域”的延伸思考。面向熟悉研究生一年级水平分析学的受众，此书的目的在于解释复变量是如何对分析的一些领域中的许多类重要结果提供了快速而高效的证明, 这些领域包括诸如近似理论、算子理论、调和分析和复动力系统。
Preface
Chapter 1． Early Triumphs
1．1． The Basel Problem
1．2． The Fundamental Theorem of Algebra
Chapter 2． Approximation
2．1． Completeness of Weighted Powers
2．2． The Muntz Approximation Theorem
Chapter 3． Operator Theory
3．1． The Fuglede-Putnam Theorem
3．2． Toeplitz Operators
3．3． A Theorem of Beurling
3．4． Prediction Theory
3．5． The Riesz-Thorin Convexity Theorem
3．6． The Hilbert Transform
Chapter 4． Harmonic Analysis
4．1． Fourier Uniqueness via Complex Variables （d'apres D．J． Newman）
4．2． A Curious Functional Equation
4．3． Uniqueness and Nonuniqueness for the Radon Transform
4．4． The Paley-Wiener Theorem
4．5． The Titchmarsh Convolution Theorem
4．6． Hardy's Theorem
……
Chapter 5． Banach Algebras： The Gleason-Kahane-Zelazko Theorem
Chapter 6． Complex Dynamics： The Fatou-Julia-Baker Theorem
Chapter 7． The Prime Number Theorem
Coda： Transonic Airfoils and SLE
Appendix A． Liouville's Theorem in Banach Spaces
Appendix B． The Borel-Caratheodory Inequality
Appendix C． Phragmen-Lindelof Theorems
Appendix D． Normal Families
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