Functions of One Complex Variable II

1. Front Matter

   Pages i-xvi

   PDF

2. Return to Basics

   • John B. Conway

   Pages 1-27

3. Conformal Equivalence for Simply Connected Regions

   • John B. Conway

   Pages 29-70

4. Conformal Equivalence for Finitely Connected Regions

   • John B. Conway

   Pages 71-107

5. Analytic Covering Maps

   • John B. Conway

   Pages 109-131

6. De Branges’s Proof of the Bieberbach Conjecture

   • John B. Conway

   Pages 133-167

7. Some Fundamental Concepts from Analysis

   • John B. Conway

   Pages 169-203

8. Harmonic Functions Redux

   • John B. Conway

   Pages 205-268

9. Hardy Spaces on the Disk

   • John B. Conway

   Pages 269-299

10. Potential Theory in the Plane

    • John B. Conway

    Pages 301-383

11. Back Matter

    Pages 384-396

    PDF

This is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat­ ical community for its reception of that work. In retrospect, writing that book was a crazy venture. As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after beginning to prepare my lectures I became dissatisfied. All the books in print had virtues; but I was educated as a modern analyst, not a classical one, and they failed to satisfy me. This set a pattern for me in learning new mathematics after I had become a mathematician. Some topics I found satisfactorily treated in some sources; some I read in many books and then recast in my own style. There is also the matter of philosophy and point of view. Going from a certain mathematical vantage point to another is thought by many as being independent of the path; certainly true if your only objective is getting there. But getting there is often half the fun and often there is twice the value in the journey if the path is properly chosen.

• Dirichlet principle
• Factor
• Nevanlinna theory
• Potential theory
• Prime
• algebra
• analytic function
• boundary element method
• convolution
• differential equation
• functions
• integration
• modular form
• subharmonic function
• variable

• Department of Mathematics, University of Tennessee, Knoxville, USA

  John B. Conway

Policies and ethics