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Function Theory of One Complex Variable, Third edition

About this Title

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

Publication: Graduate Studies in Mathematics
Publication Year: 2002; Volume 40
ISBNs: 978-0-8218-3962-1 (print); 978-1-4704-1148-0 (online)
DOI: https://doi.org/10.1090/gsm/040
MathSciNet review: MR1871333
MSC: Primary 30-01

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Table of Contents

Chapters

  • Chapter 1. Fundamental concepts
  • Chapter 2. Complex line integrals
  • Chapter 3. Applications of the Cauchy integral
  • Chapter 4. Meromorphic functions and residues
  • Chapter 5. The zeros of a holomorphic function
  • Chapter 6. Holomorphic functions as geometric mappings
  • Chapter 7. Harmonic functions
  • Chapter 8. Infinite series and products
  • Chapter 9. Applications of infinite sums and products
  • Chapter 10. Analytic continuation
  • Chapter 11. Topology
  • Chapter 12. Rational approximation theory
  • Chapter 13. Special classes of holomorphic functions
  • Chapter 14. Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings
  • Chapter 15. Special functions
  • Chapter 16. The prime number theorem
  • Appendix A. Real analysis
  • Appendix B. The statement and proof of Goursat’s theorem