书籍简介:

本书系统介绍了泛函分析的基础知识，共分为五章：度量空间、线性赋范空间与Banach空间、内积空间与Hilbert空间、Banach空间上的线性算子与基本定理，Hilbert空间上的线性算子。

书籍目录:

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

内容摘要:

　　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.

书籍规格:

书籍详细信息
书名	泛函分析导论站内查询相似图书
	9787030222268 如需购买下载《泛函分析导论》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN
出版地	北京	出版单位	科学出版社
版次	1版	印次	1
定价(元)	48.0	语种	英文
尺寸	24	装帧	平装
页数		印数

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书籍信息归属:

泛函分析导论是科学出版社于2008.出版的中图分类号为 O177 的主题关于泛函分析－英文的书籍。