Cn单位球上的函数理论

内容概要

作者:(美)鲁丁

书籍目录

List of Symbols and NotationsChapter 1Preliminaries 1.1 Some Terminology 1.2 The Cauchy Formula in Polydiscs 1.3 Differentiation 1.4 Integrals over Spheres 1.5 Homogeneous ExpansionsChapter 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 SetsChapter 3 Integral Representations 3.1 The Bergman Integral in B 3.2 The Cauchy Integral in B 3.3 The Invariant Poisson Integral in BChapter 4 The lnvariant Laplacian 4.1 The Operator 4.2 Eigenfunctions of □ 4.3 □-Harmonie Functions 4.4 Pluriharmonic FunctionsChapter 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 InterpolationChapter 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 ProblemChapter 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 TheoremChapter 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 FunctionsChapter 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 ValuesChapter 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 = 2Chapter 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 ApplicationsChapter 14 Analytic Varieties 14.1 The Weierstrass Preparation Theorem 14.2 Projections of Varieties 14.3 Compact Varieties in C" 14.4 Hausdorff MeasuresChapter 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 BChapter 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 BChapter 17 The Zeros of Nevanlinna Functions 17.1 The Henkin-Skoda Theorem 17.2 Plurisubharmonic Functions 17.3 Areas of Zero-VarietiesChapter 18 Tangential Cauchy-Riemann Operators 18.1 Extensions from the Boundary 18.2 Unsolvable Differential Equations 18.3 Boundary Values of Pluriharmonic FunctionsChapter 19 Open Problems 19.1 The Inner Function Conjecture 19.2 RP-Measures 19.3 Miscellaneous Problems Bibliography Index

编辑推荐

《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。

作者简介

《cn单位球上的函数理论》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。

目次：基础知识；b同构；积分表示；不变拉普拉斯算子；泊松积分的边界行为；柯西积分的边界行为；有关lp；施瓦兹定理结果；有关球代数测度；球代数的插值集合；h∞函数的边界行为；单位不变函数空间；moebius不变函数空间；解析变量；恰当正则映射； 问题；nevanlinna函数的零；相切canchy-riemann算子；开放问题。

读者对象：数学专业的研究生和科研人员。

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