实分析(英文)
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作者[美]斯坦恩(Stein E.M.) 著
出版社世界图书出版公司
出版时间2013-01
版次1
装帧平装
货号9787510040535
上书时间2024-08-11
商品详情
- 品相描述:八五品
图书标准信息
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作者
[美]斯坦恩(Stein E.M.) 著
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出版社
世界图书出版公司
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出版时间
2013-01
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版次
1
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ISBN
9787510040535
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定价
59.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
402页
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正文语种
英语
- 【内容简介】
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《实分析(英文)》在Princeton大学使用,同时在其它学校,比如UCLA等名校也在本科生教学中得到使用。其教学目的是,用统一的、联系的观点来把现代分析的“核心”内容教给本科生,力图使本科生的分析学课程能接上现代数学研究的脉络。
- 【目录】
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Foreword
Introduction
1Fourierseries:completion
2Limitsofcontinuousfunctions
3Lengthofcurves
4Differentiationandintegration
5Theproblemofmeasure
Chapter1.MeasureTheory
1Prelhninaries
2Theexteriormeasure
3MeasurablesetsandtheLebesguemeasure
4Measurablefunctions
4.1Definitionandbasicproperties
4.2Approximationbysimplefunctionsorstepfunctions
4.3Littlewood'sthreeprinciples
5TheBrunn-Minkowskiinequality
6Exercises
7Problems
Chapter2.IntegrationTheory
1TheLebesgueintegral:basicpropertiesandconvergencetheorems
2ThespaceL1ofintegrablefunctions
3Fubini'stheorem
3.1Statementandproofofthetheorem
3.2ApplicationsofFubini'stheorem
4*AFourierinversionformula
5Exercises
6Problems
Chapter3.DifferentiationandIntegration
1Differentiationoftheintegral
1.1TheHardy-Littlewoodmaximalfunction
1.2TheLebesguedifferentiationtheorem
2Goodkernelsandapproximationstotheidentity
3Differentiabilityoffunctions
3.1Functionsofboundedvariation
3.2Absolutelycontinuousfunctions
3.3Differentiabilityofjumpfunctions
4Rectifiablecurvesandtheisoperimetricinequality
4.1Minkowskicontentofacurve
4.2Isoperimetricinequality
5Exercises
6Problems
Chapter4.HilbertSpaces:AnIntroduction
1TheHilbertspaceL2
2Hilbertspaces
2.1Orthogonality
2.2Unitarymappings
2.3Pre-Hilbertspaces
3FourierseriesandFatou'stheorem
3.1Fatou'stheorem
4Closedsubspacesandorthogonalprojections
5Lineartransformations
5.1LinearfunctionalsandtheRieszrepresentationtheorem
5.2Adjoints
5.3Examples
6Compactoperators
7Exercises
8Problems
Chapter5.HilbertSpaces:SeveralExamples
1TheFouriertransformonL2
2TheHardyspaceoftheupperhalf-plane
3Constantcoefficientpartialdifferentialequations
3.1Weaaksolutions
3.2Themaintheoremandkeyestimate
4TheDirichletprinciple
4.1Harmonicfunctions
4.2TheboundaryvalueproblemandDirichlet'sprinciple
5Exercises
6Problems
Chapter6.AbstractMeasureandIntegrationTheory
Chapter7.HausdorffMeasureandFractals
NotesandReferences
Bibliography
SymbolGlossary
Index
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