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Tasty Bits of Several Complex Variables

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Tasty Bits of Several Complex Variables

Graduate level mathematics textbook on Several Complex Variables (complex analysis in several variables). A free online textbook based on class notes for the graduate course at Oklahoma State University.

AnalysisMathematics
Author
Jiří Lebl
Publisher
Oklahoma State University
Source
LibreTexts
License
CC BY-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 43 sections
  1. 01: Holomorphic Functions in Several Variables
  2. 1.01: Onto Several Variables
  3. 1.02: Power Series Representation
  4. 1.03: Derivatives
  5. 1.04: Inequivalence of Ball and Polydisc
  6. 1.05: Cartan's Uniqueness Theorem
  7. 1.06: Riemann Extension Theorem Zero Sets and Injective Maps
  8. 02: Convexity and Pseudoconvexity
  9. 2.01: Domains of Holomorphy and Holomorphic Extensions
  10. 2.02: Tangent Vectors the Hessian and Convexity
  11. 2.03: Holomorphic Vectors the Levi Form and Pseudoconvexity
  12. 2.04: Harmonic Subharmonic and Plurisubharmonic Functions
  13. 2.05: Hartogs Pseudoconvexity
  14. 2.06: Holomorphic Convexity
  15. 03: CR Functions
  16. 3.01: Real-Analytic Functions and Complexification
  17. 3.02: CR Functions
  18. 3.03: Approximation of CR Functions
  19. 3.04: Extension of CR Functions
  20. 04: The -Problem
  21. 4.01: The Generalized Cauchy Integral Formula
  22. 4.02: Simple Case of The -Problem
  23. 4.03: The General Hartogs Phenomenon
  24. 4.04: Solvability of -Problem in the Polydisc
  25. 05: Integral Kernels
  26. 5.01: The Bochner-Martinelli Kernel
  27. 5.02: The Bergman Kernel
  28. 5.03: The Szego Kernel
  29. 06: Complex Analytic Varieties
  30. 6.01: The Ring of Germs
  31. 6.02: Weierstrass Preparation and Division Theorems
  32. 6.03: The Dependence of Zeros on Parameters
  33. 6.04: Properties of the Ring of Germs
  34. 6.05: Varieties
  35. 6.06: Hypervarieties
  36. 6.07: Irreducibility Local Parametrization and Puiseux Theorem
  37. 6.08: Segre Varieties and CR Geometry
  38. 07: Appendix
  39. 7.01: A- Basic Notation and Terminology
  40. 7.02: B- Results from one Complex Variable
  41. 7.03: C- Differential Forms and Stokes' Theorem
  42. 7.04: D- Basic Terminology and Results from Algebra
  43. 7.5: Measure Theory Review