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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