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.

Analysis Mathematics

Tác giả: Jiří Lebl
Nhà xuất bản: Oklahoma State University
Nguồn: LibreTexts
Giấy phép: CC BY-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 43 mục

01: Holomorphic Functions in Several Variables
1.01: Onto Several Variables
1.02: Power Series Representation
1.03: Derivatives
1.04: Inequivalence of Ball and Polydisc
1.05: Cartan's Uniqueness Theorem
1.06: Riemann Extension Theorem Zero Sets and Injective Maps
02: Convexity and Pseudoconvexity
2.01: Domains of Holomorphy and Holomorphic Extensions
2.02: Tangent Vectors the Hessian and Convexity
2.03: Holomorphic Vectors the Levi Form and Pseudoconvexity
2.04: Harmonic Subharmonic and Plurisubharmonic Functions
2.05: Hartogs Pseudoconvexity
2.06: Holomorphic Convexity
03: CR Functions
3.01: Real-Analytic Functions and Complexification
3.02: CR Functions
3.03: Approximation of CR Functions
3.04: Extension of CR Functions
04: The -Problem
4.01: The Generalized Cauchy Integral Formula
4.02: Simple Case of The -Problem
4.03: The General Hartogs Phenomenon
4.04: Solvability of -Problem in the Polydisc
05: Integral Kernels
5.01: The Bochner-Martinelli Kernel
5.02: The Bergman Kernel
5.03: The Szego Kernel
06: Complex Analytic Varieties
6.01: The Ring of Germs
6.02: Weierstrass Preparation and Division Theorems
6.03: The Dependence of Zeros on Parameters
6.04: Properties of the Ring of Germs
6.05: Varieties
6.06: Hypervarieties
6.07: Irreducibility Local Parametrization and Puiseux Theorem
6.08: Segre Varieties and CR Geometry
07: Appendix
7.01: A- Basic Notation and Terminology
7.02: B- Results from one Complex Variable
7.03: C- Differential Forms and Stokes' Theorem
7.04: D- Basic Terminology and Results from Algebra
7.5: Measure Theory Review