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单复变函数（第2卷）

单复变函数（第2卷）
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作者: （John B.Conway） 著
出版社: 世界图书出版公司
2011-07
版次: 1
ISBN: 9787510037542
定价: 49.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 394页
正文语种: 英语
分类: 自然科学
2 张插图图片
70人买过
  • ThisisthesequeltomybookFunctionsofOneComplexVariableI,andprobablyagoodopportunitytoexpressmyappreciationtothemathemat-icalcommunityforitsreceptionofthatwork.Inretrospect,writingthatbookwasacrazyventure.AsagraduatestudentIhadhadoneoftheworstlearningexperiencesofmycareerwhenItookcomplexanalysis;atrulybadteacher.Asanon-tenuredassistantprofessor,thedepartmentallowedmetoteachthegraduatecourseincomplexanalysis.TheythoughtIknewthematerial;Iwantedtolearnit.IadoptedastandardtextandshortlyafterbeginningtopreparemylecturesIbecamedissatisfied.Allthebooksinprinthadvirtues;butIwaseducatedasamodernanalyst,notaclassicalone,andtheyfailedtosatisfyme. 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
  • 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
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