# Complex Proofs of Real Theorems

### About this Title

**Peter D. Lax**, *Courant Institute, New York, NY* and **Lawrence Zalcman**, *Bar-Ilan University, Ramat Gan, Israel*

Publication: University Lecture Series

Publication Year
2012: Volume 58

ISBNs: 978-0-8218-7559-9 (print); 978-0-8218-8489-8 (online)

DOI: http://dx.doi.org/10.1090/ulect/058

MathSciNet review: MR2827550

MSC: Primary 30-02; Secondary 11-02, 26-02, 46-01

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 1. Early triumphs
- Chapter 2. Approximation
- Chapter 3. Operator theory
- Chapter 4. Harmonic analysis
- Chapter 5. Banach algebras: The Gleason-Kahane-Żelazko 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-Carathéodory inequality
- Appendix C. Phragmén-Lindelöf theorems
- Appendix D. Normal families