Serge Lang ： 实分析和泛函分析

图书标准信息

• 作者 S.Lang 著
• 出版社 世界图书出版公司
• 出版时间 1997-01
• 版次 3
• ISBN 9787506233071
• 定价 92.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 580页
• 正文语种 英语

【内容简介】

　　《实分析和泛函分析（第3版）（英文版）》ismeantasatextforafirstyeargraduatecourseinanalysis.Anystandardcourseinundergraduateanalysiswillconstitutesufficientpreparationforitsunderstanding，forinstance，myUndergraduateAnalysis.Iassumethatthereaderisacquaintedwithnotionsofuniformconvergenceandthelike.
　　Inthisthirdedition，Ihavereorganizedthebookbycoveringintegrationbeforefunctionalanalysis.SucharearrangementfitsthewaycoursesaretaughtinalltheplacesIknowof.Ihaveaddedanumberofexamplesandexercises，aswellassomematerialaboutintegrationontherealline（e.g.onDiracsequenceapproximationandonFourieranalysis），andsomematerialonfunctionalanalysis（e.g.thetheoryoftheGelfandtransforminChapterXVI）.Theseupgradepreviousexercisestosectionsinthetext.

【目录】

PARTONE
GeneralTopology
CHAPTERⅠ
Sets
l.SomeBasicTerminology
2.DenumerableSets
3.Zorn'sLemma
CHAPTERⅡ
TopologicalSpaces
1.OpenandClosedSets
2.ConnectedSets
3.CompactSpaces
4.SeparationbyContinuousFunctions
5.Exercises
CHAPTERⅢ
ContinuousFunctionsonCompactSets
l.TheStone-WeierstrassTheorem
2.IdealsofContinuousFunctions
3.Ascoli'sTheorem
4.Exercises

PARTTWO
BanachandHilbertSpaces
CHAPTERIV
BanachSpaces
1.Definitions，theDualSpace，andtheHahn-BanachTheorem
2.BanachAlgebras
3.TheLinearExtensionTheorem
4.CompletionofaNormedVectorSpace
5.SpaceswithOperators
Appendix：ConvexSets
I.TheKrein-MilmanTheorem
2.Mazur'sTheorem
6.Exercises
CHAPTERV
HilbertSpace
1.HermitianForms
2.FunctionalsandOperators
3.Exercises

PARTTHREE
Integration
CHAPTERⅣ
TheGeneralIntegral
1.MeasuredSpaces，MeasurableMaps，aridPositiveMeasures
2.TheIntegralofStepMaps
3.TheL1-Completion
4.PropertiesoftheIntegral：FirstPart
5.PropertiesoftheIntegral：SecondPart
6.Approximations
7.ExtensionofPositiveMeasuresfromAlgebrastoa-Algebras
8.ProductMeasuresandIntegrationonaProductSpace
9.TheLebesgueIntegralinRp
10.Exercises
CHAPTERⅦ
DualityandRepresentationTheorems
1.TheHilbertSpaceL2（μ）
2.DualityBetweenL1（μ）andL∞（μ）
3.ComplexandVectorialMeasures
4.ComplexorVectorialMeasuresandDuality
5.TheLpSpaces，16.TheLawofLargeNumbers
7.Exercises
CHAPTERⅧ
SomeApplicationsofIntegration
1.Convolution
2.ContinuityandDifferentiationUndertheIntegralSign
3.DiracSequences
4.TheSchwartzSpaceandFourierTransform
5.TheFourierInversionFormula
6.ThePoissonSummationFormula
7.AnExampleofFourierTransformNotintheSchwartzSpace
8.Exercises
CHAPTERⅨ
IntegrationandMeasuresonLocallyCompactSpaces
1.PositiveandBoundedFunctionalsonCc（X）
2.PositiveFunctionalsasIntegrals
3.RegularPositiveMeasures
4.BoundedFunctionalsasIntegrals
5.LocalizationofaMeasureandoftheIntegral
6.ProductMeasuresonLocallyCompactSpaces
7.Exercises
CHAPTERⅩ
Riemann-StieltjesIntegralandMeasure
l.FunctionsofBoundedVariationandtheStiehjesIntegral
2.ApplicationstoFourierAnalysis
3.Exercises
CHAPTERXl
Distributions
1.DefinitionandExamples
2.SupportandLocalization
3.DerivationofDistributions
4.DistributionswithDiscreteSupport
CHAPTERⅫ
IntegrationonLocallyCompactGroups
l.TopologicalGroups
2.TheHaarIntegral，Uniqueness
3.ExistenceoftheHaarIntegral
4.MeasuresonFactorGroupsandHomogeneousSpaces
5.Exercises

PARTFOUR
Calculus
CHAPTERⅩⅢ
DifferentialCalculus
1.IntegrationinOneVariable
2.TheDerivativeasaLinearMap
3.PropertiesoftheDerivative
4.MeanValueTheorem
5.TheSecondDerivative
6.HigherDerivativesandTaylor'sFormula
7.PartialDerivatives
8.DifferentiatingUndertheIntegralSign
9.DifferentiationofSequences
10.Exercises
CHAPTERⅩⅣ
InverseMappingsandDifferentialEquations
1.TheInverseMappingTheorem
2.TheImplicitMappingTheorem
3.ExistenceTheoremforDifferentialEquations
4.LocalDependenceonInitialConditions
5.GlobalSmoothnessoftheFlow
6.Exercises

PARTFIVE
FunctionalAnalysis
CHAPTERXV
TheOpenMappingTheorem，FactorSpaces，andDuality
1.TheOpenMappingTheorem
2.Orthogonality
3.ApplicationsoftheOpenMappingTheorem
CHAPTERXVl
TheSpectrum
1.TheGelfand-MazurTheorem
2.TheGelfandTransform
3.C*-Algebras
4.Exercises
CHAPTERXVll
CompactandFredholmOperators
1.CompactOperators
2.FredholmOperatorsandtheIndex
3.SpectralTheoremforCompactOperators
4.ApplicationtoIntegralEquations
5.Exercises
……
PARTSIX
Index