单复变函数（第2卷）

图书标准信息

• 作者 康韦（John B.Conway） 著
• 出版社 世界图书出版公司
• 出版时间 2011-07
• 版次 1
• ISBN 9787510037542
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 394页
• 正文语种 英语

【内容简介】

ThisisthesequeltomybookFunctionsofOneComplexVariableI,andprobablyagoodopportunitytoexpressmyappreciationtothemathemat-icalcommunityforitsreceptionofthatwork.Inretrospect,writingthatbookwasacrazyventure.AsagraduatestudentIhadhadoneoftheworstlearningexperiencesofmycareerwhenItookcomplexanalysis;atrulybadteacher.Asanon-tenuredassistantprofessor,thedepartmentallowedmetoteachthegraduatecourseincomplexanalysis.TheythoughtIknewthematerial;Iwantedtolearnit.IadoptedastandardtextandshortlyafterbeginningtopreparemylecturesIbecamedissatisfied.Allthebooksinprinthadvirtues;butIwaseducatedasamodernanalyst,notaclassicalone,andtheyfailedtosatisfyme.

【目录】

Preface
13ReturntoBasics
1RegionsandCurves
2DerivativesandOtherRecollections
3HarmonicConjugatesandPrimitives
4AnalyticArcsandtheReflectionPrinciple
5BoundaryValuesforBoundedAnalyticFunctions

14ConformalEquivalenceforSimplyConnectedRegions
1ElementaryPropertiesandExamples
2Crosscuts
3PrimeEnds
4ImpressionsofaPrimeEnd
5BoundaryValuesofRiemannMaps
6TheAreaTheorem
7DiskMappings:TheClass

15ConformalEquivalenceforFinitelyConnectedRegions
IAnalysisonaFinitelyConnectedRegion
2ConformalEquivalencewithanAnalyticJordanRegion
3BoundaryValuesforaConformalEquivalenceBetweenFinitelyConnectedJordanRegions
4ConvergenceofUnivalentFunctions
5ConformalEquivalencewithaCircularlySlitAnnulus
6ConformalEquivalencewithaCircularlySlitDisk
7ConformalEquivalencewithaCircularRegion

16AnalyticCoveringMaps
1ResultsforAbstractCoveringSpaces
2AnalyticCoveringSpaces
3TheModularFunction
4ApplicationsoftheModularFunction
5TheExistenceoftheUniversalAnalyticCoveringMap

17DeBranges'sProofoftheBieberbachConjecture
1Subordination
2LoewnerChains
3Loewner'sDifferentialEquation
4TheMilinConjecture
5SomeSpecialFunctions
6TheProofofdeBranges'sTheorem

18SomeFundamentalConceptsfromAnalysis
1BergmanSpacesofAnalyticandHarmonicFunctions
2PartitionsofUnity
3ConvolutioninEuclideanSpace
4Distributions
5TheCauchyTransform
6AnApplication:RationalApproximation
7FourierSeriesandCesaroSums

19HarmonicFunctionsRedux
1HarmonicFunctionsontheDisk
2Fatou'sTheorem
3SemicontinuousFunctions
4SubharmonicFunctions
5TheLogarithmicPotential
6AnApplication:ApproximationbyHarmonicFunctions
7TheDirichletProblem
8HarmonicMajorants
9TheGreenFunction
10RegularPointsfortheDirichletProblem
11TheDirichletPrincipleandSobolevSpaces

20HardySpacesontheDisk
1DefinitionsandElementaryProperties
2TheNevanlinnaClass
3FactorizationofFunctionsintheNevanlinnaClass
4TheDiskAlgebra
5TheInvariantSubspacesofHp
6Szego'sTheorem

21PotentialTheoryinthePlane
1HarmonicMeasure
2TheSweepofaMeasure
3TheRobinConstant
4TheGreenPotential
5PolarSets
6MoreonRegularPoints
7LogarithmicCapacity:Part1
8SomeApplicationsandExamplesofLogarithmicCapacity
9RemovableSingularitiesforFunctionsintheBergmanSpace
10LogarithmicCapacity:Part2
11TheTransfiniteDiameterandLogarithmicCapacity
12TheRefinementofaSubharmonicFunction
13TheFineTopology
14Wiener'scriterionforRegularPoints
Contents
References
ListofSymbols
Index