泛函分析导论英文版
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作者Yisheng Huang 著
出版社科学出版社
出版时间2009-01
版次1
装帧平装
货号165
上书时间2024-12-19
商品详情
- 品相描述:八五品
图书标准信息
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作者
Yisheng Huang 著
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出版社
科学出版社
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出版时间
2009-01
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版次
1
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ISBN
9787030222268
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定价
58.00元
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装帧
平装
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开本
16开
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纸张
胶版纸
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页数
229页
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正文语种
英语
- 【内容简介】
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Functionalanalysisisprimarilyconcernedwithinfinite-dimensionallinear(vector)spaces,mainlyfunctionspaceswhose"points"arefunctions,andmappingsbetweenthem,usuallycalledoperatorsor,functionalsiftherangeisonthereallineorinthecomplexplane.Itwasinventedanddevelopedinthelastyearsofthenineteenthcenturyandthefirstfewdecadesofthetwentiethcentury.Duringtheearlyperiodofitsdevelopment,theoriginalpurposeoffunctionalanalysiswastouseaframeworkwhichallowsthestudyofdifferentialandintegralequationstobeconsideredinthesameformulation(cf.[6]).Later,functionalanalysisdevelopedrapidlyasin-depthstudyandin-terconnectiononspectraltheoryofordinaryandpartialdifferentialequations,potentialtheory,Fourierexpansions,andappliedmathematicaltechniques,especially,ontheinfluenceofmathematicalphysicsandquantummechan-ics.
- 【目录】
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Preface
ListofSymbols
Chapter1MetricSpaces
1.1Preliminaries
1.2DefinitionsandExamples
1.3ConvergenceinaMetricSpace
1.4SetsinaMetricSpace
1.5CompleteMetricSpaces
1.6ContinuousMappingsonMetricSpaces
1.7CompactMetricSpaces
1.8TheContractionMappingPrinciple
Chapter2NormedLinearSpaces.BanachSpaces
2.1ReviewofLinearSpaces
2.2NorminaLinearSpace
2.3ExamplesofNormedLinearSpaces
2.4FiniteDimensionalNormedLinearSpaces
2.5LinearSubspacesofNormedLinearSpaces
2.6QuotientSpaces
2.7TheWeierstrassApproximationTheorem
Chapter3InnerProductSpaces.HilbertSpaces
3.1InnerProducts
3.2Orthogonality
3.3OrthonormalSystems
3.4FourierSeries
Chapter4LinearOperators.FundamentalTheorems
4.1ContinuousLinearOperatorsandFunctionals
4.2SpacesofBoundedLinearOperatorsandDualSpaces
4.3TheBanach-SteinhausTheorem
4.4InversesofOperators.TheBanachTheorem
4.5TheHahn-BanachTheorem
4.6StrongandWeakConvergence
Chapter5LinearOperatorsonHilbertSpaces
5.1AdjointOperators.TheLax-MilgramTheorem
5.2SpectralTheoremforSelf-adjointCompactOperators
Bibliography
Index
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