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Tuesday 24 July 2012

Function Theory of One Complex Variable (Third Edition) Greene, Robert E & Krantz, Steven G

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Function Theory of One Complex Variable (Third Edition)
Greene, Robert E & Krantz, Steven G
2011; 528 pp; Paperback; 180 × 240 mm; 978-0-8218-6877-5
For sale only in India,Pakistan,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives
Series: Indian Editions of AMS Titles
895.00
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point.
The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat $H^p$ spaces and Painlevé''''s theorem on smoothness to the boundary for conformal maps.
This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors'''' expertise both as mathematicians and as expositors

Table of Contents
Preface to the Third Edition
Preface to the Second Edition 
Preface to the First Edition
Acknowledgements
  1. Fundamental Concepts
  2. Complex Line Integrals
  3. Applications of the Cauchy Integral
  4. Meromorphic Functions and Residues
  5. The Zeros of a Holomorphic Function
  6. Holomorphic Functions as Geometric Mappings
  7. Harmonic Functions
  8. Infinite Series and Products
  9. Applications of Infinite Sums and Products
  10. Analytic Continuation
  11. Topology
  12. Rational Approximation Theory
  13. Special Classes of Holomorphic Functions
  14. Hilbert Spaces of Holomorphic Functions, the Bergman Kernel, and Biholomorphic Mappings
  15. Special Functions
  16. The Prime Number Theorem
Appendix A
Appendix B
References
Index

About the AUthor
Robert E. Greene, University of California, Los Angeles, CA, and Steven G. Krantz, Washington University, St. Louis, MO

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