泛函分析导论（英文版）

图书标准信息

• 作者 Yisheng Huang 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030222268
• 定价 58.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 229页
• 正文语种 英语

【内容简介】

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】

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