Complex Analysis: A Functional Analysis Approach

✍ Scribed by D.H. Luecking, L.A. Rubel

• Publisher: Springer
• Year: 1984
• Tongue: English
• Leaves: 184
• Series: Universitext
• Category: Library

✦ Table of Contents

Title......Page 3
Introduction......Page 5
Contents......Page 7
1. Preliminaries: Set Theory and Topology......Page 9
2. Preliminaries: Vector Spaces and Complex Variables......Page 21
3. Properties of C(G) and H(G)......Page 35
4. More About C(G) and H(G)......Page 41
5. Duality......Page 46
6. Duality of H(G) - The Case of the Unit Disc......Page 52
7. The Hahn-Banach Theorem, and Applications......Page 59
8. More Applications......Page 68
9. The Dual of H(G)......Page 75
10. Runge's Theorem......Page 85
11. The Cauchy Theorem......Page 92
12. Constructive Function Theory......Page 104
13. Ideals in H(G)......Page 116
14. The Riemann Mapping Theorem......Page 125
15. Caratheodory Kernels and Farrell's Theorem......Page 132
16. Ring (not Algebra) Isomorphisms of H(G)......Page 138
17. Dual Space Topologies......Page 144
18. Interpolation......Page 159
19. Gap-Interpolation Theorems......Page 165
20. First-Order Conformal Invariants......Page 176
References......Page 182