Cn单位球上的函数理论
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作者(美)鲁丁
出版社世界图书出版公司
ISBN9787510052699
出版时间2013-01
装帧其他
开本其他
定价79元
货号2432236
上书时间2024-05-25
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导语摘要
《Cn单位球上的函数理论》(作者鲁丁)是springer数学经典教材系列之一，表述清晰易懂，自然流畅，用很少的实分析、复分析和泛函分析基本知识做铺垫，全面介绍了球上基本原理。既是一本很好的参考书，又是一本高年级教程。
目录
List of Symbols and Notations
Chapter 1
Preliminaries
1.1 Some Terminology
1.2 The Cauchy Formula in Polydiscs
1.3 Differentiation
1.4 Integrals over Spheres
1.5 Homogeneous Expansions
Chapter 2
The Automorphisms of B
2.1 Cartan's Uniqueness Theorem
2.2 The Automorphisms
2.3 The Cayley Transform
2.4 Fixed Points and Afline Sets
Chapter 3
Integral Representations
3.1 The Bergman Integral in B
3.2 The Cauchy Integral in B
3.3 The Invariant Poisson Integral in B
Chapter 4
The lnvariant Laplacian
4.1 The Operator
4.2 Eigenfunctions of □
4.3 □-Harmonie Functions
4.4 Pluriharmonic Functions
Chapter 5
Boundary Behavior of Poisson Integrals
5.1 A Nonisotropic Metric on S
5.2 The Maximal Function of a Measure on S
5.3 Differentiation of Measures on S
5.4 K-Limits of Poisson Integrals
5.5 Theorems of Calder6n. Privalov, Plessner
5.6 The Spaces N(B) and H□(B)
5.7 Appendix: Marcinkiewicz Interpolation
Chapter 6
Boundary Behavior of Cauchy Integrals
6,1 An Inequality
6.2 Cauchy Integrals of Measures
6.3 Cauchy Integrals of LP-Functions
6.4 Cauchy Integrals of Lipschltz Functions
6.5 Toeplitz Operators
6.6 Gleason's Problem
Chapter 7
Some LP-Topics
7.1 Projections of Bergman Type
7.2 Relations between Hp and Lp□H
7.3 Zero-Varieties
7.4 Pluriharmonic Majoranls
7.5 The Isometties of HP(B)
Chapter 8
Consequences of the Schwarz Lemma
8.1 The Schwarz Lemma in B
8.2 Fixed-Point Sets in B
8.3 An Extension Problem
8.4 The Liodel6f-□irka Theorem
8,5 The Julia-Carath6odory Theorem
Chapter 9
Measures Related to the Ball Algebra
9.1 Introduction
9.2 Valskii's Decomposition
9.3 Henkin's Theorem
9.4 A General Lebesgue Decomposition
9.5 A General F. and M. Riesz Theorem
9.6 The Cole-Range Theorem
9.7 Pluriharmonic Majorants
9.8 The Dual Space of A(B)
Chapter 10
Interpolation Sets for the Ball Algebra
10.1 Some Equivalences
10.2 A Theorem of Varopoulos
10.3 A Theorem of Bishop
10.4 The Davie-□ksendal Theorem
10.5 Smooth Interpolation Sets
10.6 Determining Sets
10.7 Peak Sets for Smooth Functions
Chapter 11
Boundary Behavior of H□-Functions
11.1 A Fatou Theorem in One Variable
11.2 Boundary Values on Curves in S
11.3 Weak*-Convergence
11.4 A Problem on Extreme Values
Chapter 12
Unitarily Invariant Function Spaces
12.1 Spherical Harmonics
12.2 The Spaces H~, q)
12.3 □-Invariant Spaceson S
12.4 □-lnvariant Subalgebras of C(S)
12.5 The Case n = 2
Chapter 13
Moebius-lnvariant Function Spaces
13.1 □-Invariant Spaces on S
13.2 □-Invariant Subalgebras of Co(B)
13.3 □-lnvariant Subspaces of C(□)
13.4 Some Applications
Chapter 14
Analytic Varieties
14.1 The Weierstrass Preparation Theorem
14.2 Projections of Varieties
14.3 Compact Varieties in C"
14.4 Hausdorff Measures
Chapter 15
Proper Holomorphic Maps
15.1 The Structure of Proper Maps
15.2 Balls vs. Polydiscs
15.3 Local Theorems
15.4 Proper Maps from B to B
15.5 A Characterization of B
Chapter 16
The □-problem
16.1 Differential Forms
16.2 Differential Forms in C"
16.3 The □-problem with Compact Support
16.4 Some Computations
16.5 Koppelman's Cauchy Formula
16.6 The g-problem in Convex Regions
16.7 An Explicit Solution in B
Chapter 17
The Zeros of Nevanlinna Functions
17.1 The Henkin-Skoda Theorem
17.2 Plurisubharmonic Functions
17.3 Areas of Zero-Varieties
Chapter 18
Tangential Cauchy-Riemann Operators
18.1 Extensions from the Boundary
18.2 Unsolvable Differential Equations
18.3 Boundary Values of Pluriharmonic Functions
Chapter 19
Open Problems
19.1 The Inner Function Conjecture
19.2 RP-Measures
19.3 Miscellaneous Problems
Bibliography
Index
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