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Complex Analysis : An Invitation - Murali Rao

Complex Analysis

An Invitation

By: Murali Rao, Soren Fournais, Jacob Schach Moller, Henrik Stetkaer

eText | 28 January 2015 | Edition Number 2

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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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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
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Non-FictionMathematicsCalculus & Mathematical AnalysisComplex Analysis

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Hardcover

Published: 29th January 2015

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