复分析中的不等式（影印版）

样章

作者：

John P. D'Angelo

定价：

135.00 元

版面字数：

478千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2022年

ISBN：

978-7-04-057033-5

物料号：

57033-00

出版时间：

2022-02-28

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

目录
- 前辅文
- I Complex Numbers
  - I.1 The real number system
  - I.2 Definition of the complex number field
  - I.3 Elementary complex geometry
  - I.4 Alternative definitions of the complex numbers
  - I.5 Completeness
  - I.6 Convergence for power series
  - I.7 Trigonometry
  - I.8 Roots of unity
  - I.9 Summary
- II Complex Euclidean Spaces and Hilbert Spaces
  - II.1 Hermitian inner products
  - II.2 Orthogonality, projections and closed subspaces
  - II.3 Orthonormal expansion
  - II.4 The polarization identity
  - II.5 Generating functions and orthonormal systems
- III Complex Analysis in Several Variables
  - III.1 Holomorphic functions
  - III.2 Some calculus
  - III.3 The Bergman kernel function
- IV Linear Transformations and Positivity Conditions
  - IV.1 Adjoints and Hermitian forms
  - IV.2 Solving linear equations
  - IV.3 Linearization
  - IV.4 Eigenvalues and the spectral theorem in finite dimensions
  - IV.5 Positive definite linear transformations in finite dimensions
  - IV.6 Hilbert’s inequality
  - IV.7 Additional inequalities from Fourier analysis
- V Compact and Integral Operators
  - V.1 Convergence properties for bounded linear transformations
  - V.2 Compact operators on Hilbert space
  - V.3 The spectral theorem for compact Hermitian operators
  - V.4 Integral operators
  - V.5 A glimpse at singular integral operators
- VI Positivity Conditions for Real-valued Functions
  - VI.1 Real variables analogues
  - VI.2 Real-valued polynomials on Cn
  - VI.3 Squared norms and quotients of squared norms
  - VI.4 Plurisubharmonic functions
  - VI.5 Positivity conditions for polynomials
- VII Stabilization and Applications
  - VII.1 Stabilization for positive bihomogeneous polynomials
  - VII.2 Positivity everywhere
  - VII.3 Positivity on the unit sphere
  - VII.4 Applications to proper holomorphic mappings between balls
  - VII.5 Positivity on zero sets
  - VII.6 Proof of stabilization
- VIII Afterword
- Appendix A
  - A.1 Algebra
  - A.2 Analysis
- Bibliography
- Index