Complex Analysis: An Invitation

By: Rao, MuraliContributor(s): Stetkaer, Henrik | Fournais, Soren | Mollar, Jacob SchachMaterial type: TextTextLanguage: English Publication details: Singapore World Scientific 2022Edition: 2ndDescription: x, 414pISBN: 9781944659943 (PB)Subject(s): Harmonic functions | Global theory | Mathematics
Contents:
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
Summary: 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.
Item type: BOOKS List(s) this item appears in: New Arrivals (01 April 2024)
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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.

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The Institute of Mathematical Sciences, Chennai, India

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