Cn单位球上的函数理论

图书标准信息

• 作者 [美]鲁丁 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 1
• ISBN 9787510052699
• 定价 79.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 436页

【内容简介】

　　《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】

ListofSymbolsandNotations
Chapter1
Preliminaries
1.1SomeTerminology
1.2TheCauchyFormulainPolydiscs
1.3Differentiation
1.4IntegralsoverSpheres
1.5HomogeneousExpansions
Chapter2
TheAutomorphismsofB
2.1Cartan'sUniquenessTheorem
2.2TheAutomorphisms
2.3TheCayleyTransform
2.4FixedPointsandAflineSets
Chapter3
IntegralRepresentations
3.1TheBergmanIntegralinB
3.2TheCauchyIntegralinB
3.3TheInvariantPoissonIntegralinB
Chapter4
ThelnvariantLaplacian
4.1TheOperator
4.2Eigenfunctionsof□
4.3□-HarmonieFunctions
4.4PluriharmonicFunctions
Chapter5
BoundaryBehaviorofPoissonIntegrals
5.1ANonisotropicMetriconS
5.2TheMaximalFunctionofaMeasureonS
5.3DifferentiationofMeasuresonS
5.4K-LimitsofPoissonIntegrals
5.5TheoremsofCalder6n.Privalov,Plessner
5.6TheSpacesN（B）andH□（B）
5.7Appendix:MarcinkiewiczInterpolation
Chapter6
BoundaryBehaviorofCauchyIntegrals
6,1AnInequality
6.2CauchyIntegralsofMeasures
6.3CauchyIntegralsofLP-Functions
6.4CauchyIntegralsofLipschltzFunctions
6.5ToeplitzOperators
6.6Gleason'sProblem
Chapter7
SomeLP-Topics
7.1ProjectionsofBergmanType
7.2RelationsbetweenHpandLp□H
7.3Zero-Varieties
7.4PluriharmonicMajoranls
7.5TheIsomettiesofHP（B）
Chapter8
ConsequencesoftheSchwarzLemma
8.1TheSchwarzLemmainB
8.2Fixed-PointSetsinB
8.3AnExtensionProblem
8.4TheLiodel6f-□irkaTheorem
8,5TheJulia-Carath6odoryTheorem
Chapter9
MeasuresRelatedtotheBallAlgebra
9.1Introduction
9.2Valskii'sDecomposition
9.3Henkin'sTheorem
9.4AGeneralLebesgueDecomposition
9.5AGeneralF.andM.RieszTheorem
9.6TheCole-RangeTheorem
9.7PluriharmonicMajorants
9.8TheDualSpaceofA（B）
Chapter10
InterpolationSetsfortheBallAlgebra
10.1SomeEquivalences
10.2ATheoremofVaropoulos
10.3ATheoremofBishop
10.4TheDavie-□ksendalTheorem
10.5SmoothInterpolationSets
10.6DeterminingSets
10.7PeakSetsforSmoothFunctions
Chapter11
BoundaryBehaviorofH□-Functions
11.1AFatouTheoreminOneVariable
11.2BoundaryValuesonCurvesinS
11.3Weak*-Convergence
11.4AProblemonExtremeValues
Chapter12
UnitarilyInvariantFunctionSpaces
12.1SphericalHarmonics
12.2TheSpacesH~,q）
12.3□-InvariantSpacesonS
12.4□-lnvariantSubalgebrasofC（S）
12.5TheCasen=2
Chapter13
Moebius-lnvariantFunctionSpaces
13.1□-InvariantSpacesonS
13.2□-InvariantSubalgebrasofCo（B）
13.3□-lnvariantSubspacesofC（□）
13.4SomeApplications
Chapter14
AnalyticVarieties
14.1TheWeierstrassPreparationTheorem
14.2ProjectionsofVarieties
14.3CompactVarietiesinC"
14.4HausdorffMeasures
Chapter15
ProperHolomorphicMaps
15.1TheStructureofProperMaps
15.2Ballsvs.Polydiscs
15.3LocalTheorems
15.4ProperMapsfromBtoB
15.5ACharacterizationofB
Chapter16
The□-problem
16.1DifferentialForms
16.2DifferentialFormsinC"
16.3The□-problemwithCompactSupport
16.4SomeComputations
16.5Koppelman'sCauchyFormula
16.6Theg-probleminConvexRegions
16.7AnExplicitSolutioninB
Chapter17
TheZerosofNevanlinnaFunctions
17.1TheHenkin-SkodaTheorem
17.2PlurisubharmonicFunctions
17.3AreasofZero-Varieties
Chapter18
TangentialCauchy-RiemannOperators
18.1ExtensionsfromtheBoundary
18.2UnsolvableDifferentialEquations
18.3BoundaryValuesofPluriharmonicFunctions
Chapter19
OpenProblems
19.1TheInnerFunctionConjecture
19.2RP-Measures
19.3MiscellaneousProblems
Bibliography
Index