复分析中的不等式（影印版）

样章

作者：

John P. D'Angelo

定价：

135.00元

ISBN：

978-7-04-057033-5

版面字数：

478.000千字

开本：

特殊

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

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

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