Tasty Bits of Several Complex Variables VNMV985MXX

URI	`m2://res/VNMV985MXX`
Kind	textbook
Creators	Jiří Lebl
Scope	deferred (no test decides the record, and the classifier has no model)

Expressions

e1: edition

Contents

chapter: Introduction
section 1: Motivation, single variable, and Cauchy's formula
chapter 1: Holomorphic Functions in Several Variables
section 1.1: Onto several variables
section 1.2: Power series representation
section 1.3: Derivatives
section 1.4: Inequivalence of ball and polydisc
section 1.5: Cartan's uniqueness theorem
section 1.6: Riemann extension, zero sets, and injective maps
chapter 2: Convexity and Pseudoconvexity
section 2.1: Domains of holomorphy \& holomorphic extension
section 2.2: Tangent vectors, the Hessian, and convexity
section 2.3: Holomorphic vectors, Levi form, pseudoconvexity
section 2.4: From harmonic to plurisubharmonic functions
section 2.5: Hartogs pseudoconvexity
section 2.6: Holomorphic convexity
chapter 3: CR Functions
section 3.1: Real-analytic functions and complexification
section 3.2: CR functions
section 3.3: Approximation of CR functions
section 3.4: Extension of CR functions
chapter 4: The \texorpdfstring{$\bar{\partial}$}{dbar}-problem
section 4.1: The generalized Cauchy integral formula
section 4.2: Compactly supported \texorpdfstring{$\bar{\partial}$}{dbar}-problem
section 4.3: The general Hartogs phenomenon
section 4.4: Solvability of the \texorpdfstring{$\bar{\partial}$}{dbar}-problem in the polydisc
section 4.5: Extension from an affine subspace
section 4.6: The Cousin problems
chapter 5: Integral Kernels
section 5.1: The Bochner--Martinelli kernel
section 5.2: The Bergman kernel
section 5.3: The Szeg{\H{o}} kernel
chapter 6: Complex Analytic Varieties
section 6.1: The ring of germs
section 6.2: Weierstrass preparation and division theorems
section 6.3: The dependence of zeros on parameters
section 6.4: Properties of the ring of germs
section 6.5: Varieties
section 6.6: Hypervarieties
section 6.7: Irreducibility, local parametrization, and Puiseux
section 6.8: Segre varieties and CR geometry
appendix A: Basic Notation and Terminology
appendix B: Results from One Complex Variable
appendix C: Differential Forms and Stokes' Theorem
appendix D: Basic Terminology and Results from Algebra
appendix E: Results From Real Analysis
section E.1: Measure theory review
section E.2: Classical convexity
section E.3: Smooth bump functions and partitions of unity

Catalogue records

lebl_scv: lebl_scv (work)