| Author: | Murali Rao, Henrik Stetkær, Søren Fournais;Jacob Schach Møller | ISBN: | 9789814579612 |
| Publisher: | World Scientific Publishing Company | Publication: | January 28, 2015 |
| Imprint: | WSPC | Language: | English |
| Author: | Murali Rao, Henrik Stetkær, Søren Fournais;Jacob Schach Møller |
| ISBN: | 9789814579612 |
| Publisher: | World Scientific Publishing Company |
| Publication: | January 28, 2015 |
| Imprint: | WSPC |
| Language: | English |
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.
Contents:
- Power Series
- Holomorphic and Analytic Functions
- Exponential Function, Logarithm and Winding Number
- Basic Theory of Holomorphic Functions
- Global Theory
- Isolated Singularities
- The Picard Theorems
- Geometric Aspects and the Riemann Mapping Theorem
- Meromorphic Functions and Runge's Theorems
- Representations of Meromorphic Functions
- The Prime Number Theorem
- Harmonic Functions
- Subharmonic Functions
- Various Applications
- Jordan Regions
- The Dirichlet Problem and Green's Functions
- Extending Riemann Maps to the Boundary
- Carathéodory Convergence
- Capacities
- Loewner Theory
Readership: Advanced undergraduates and graduate students of mathematics including mathematicians interested in Loewner theory.
Key Features:
- It contains an accessible introduction to the results and techniques of complex function theory with recent simplifications
- It discusses compact hulls, half-plane hulls and their capacities. Examples are computed in detail
- It contains recent results in Loewner theory and proofs of them, not just in the disc, but also in the half-plane
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.
Contents:
- Power Series
- Holomorphic and Analytic Functions
- Exponential Function, Logarithm and Winding Number
- Basic Theory of Holomorphic Functions
- Global Theory
- Isolated Singularities
- The Picard Theorems
- Geometric Aspects and the Riemann Mapping Theorem
- Meromorphic Functions and Runge's Theorems
- Representations of Meromorphic Functions
- The Prime Number Theorem
- Harmonic Functions
- Subharmonic Functions
- Various Applications
- Jordan Regions
- The Dirichlet Problem and Green's Functions
- Extending Riemann Maps to the Boundary
- Carathéodory Convergence
- Capacities
- Loewner Theory
Readership: Advanced undergraduates and graduate students of mathematics including mathematicians interested in Loewner theory.
Key Features:
- It contains an accessible introduction to the results and techniques of complex function theory with recent simplifications
- It discusses compact hulls, half-plane hulls and their capacities. Examples are computed in detail
- It contains recent results in Loewner theory and proofs of them, not just in the disc, but also in the half-plane
