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Rao, Murali

Complex Analysis: An Invitation - 2nd - Singapore World Scientific 2022 - x, 414p.

Includes bibliographical references (pages 310-325) and index

1. Power Series
2. Holomorphic and Analytic Functions
3. Exponential Function, Logarithm and Winding Number
4. Basic Theory of Holomorphic Functions
5. Global Theory
6. Isolated Singularities
7. The Picard Theorems
8. Geometric Aspects and the Riemann Mapping Theorem
9. Meromorphic Functions and Runge's Theorems
10. Representations of Meromorphic Functions
11. The Prime Number Theorem
12. Harmonic Functions
13. Subharmonic Functions
14. Various Applications
15. Jordan Regions
16. The Dirichlet Problem and Green's Functions
17. Extending Riemann Maps to the Boundary
18. Caratheodory Convergence
19. Capacities
20. Loewner Theory

This volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.

ISBN: 9781944659943 (PB)

Subjects--Topical Terms:
Harmonic functions
Global theory

Universal Decimal Class. No.: 517.53 / RAO