《Cn 單位球上的函式理論》是2013年世界圖書出版公司北京公司出版的著作，作者是魯丁 (Walter Rudin)。
基本介紹
- 中文名：《Cn 單位球上的函式理論》
- 作者：魯丁 (Walter Rudin)
- 出版時間：2013年1月1日
- 出版社：世界圖書出版公司北京公司
- ISBN：9787510052699
內容簡介,目錄,
內容簡介
《cn單位球上的函式理論》是springer數學經典教材系列之一，表述清晰易懂，自然流暢，用很少的實分析、複分析和泛函分析基本知識做鋪墊，全面介紹了球上基本原理。既是一本很好的參考書，又是一本高年級教程。
目次：基礎知識；b同構；積分表示；不變拉普拉斯運算元；泊松積分的邊界行為；柯西積分的邊界行為；有關lp；施瓦茲定理結果；有關球代數測度；球代數的插值集合；h∞函式的邊界行為；單位不變函式空間；moebius不變函式空間；解析變數；恰當正則映射； 問題；nevanlinna函式的零；相切canchy-riemann運算元；開放問題。
讀者對象：數學專業的研究生和科研人員。
目錄
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
