应用泛函分析（第2卷）（英文版）

图书标准信息

• 作者 [德]泽德勒 著
• 出版社 世界图书出版公司
• 出版时间 2009-10
• 版次 1
• ISBN 9787510005459
• 定价 49.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 404页
• 正文语种 英语

【内容简介】

　　Moreprecisely，by（i），Imeanasystematicpresentationofthematerialgovernedbythedesireformathematicalperfectionandcompletenessoftheresults.Incontrastto（i），approach（ii）startsoutfromthequestion"Whatarethemostimportantapplications？"andthentriestoanswerthisquestionasquicklyaspossible.Here，onewalksdirectlyonthemainroadanddoesnotwanderintoalltheniceandinterestingsideroads.
　　Thepresentbookisbasedonthesecondapproach.Itisaddressedtoundergraduateandbeginninggraduatestudentsofmathematics，physics，andengineeringwhowanttolearnhowfunctionalanalysiselegantlysolvesma~hematicalproblemsthatarerelatedtoourrealworldazldthathaveplayedanimportantroleinthehistoryofmathematics.Thereadershouldsensethatthetheoryisbeingdeveloped，notsimplyforitsownsake，butfortheeffectivesolutionofconcreteproblems.

【作者简介】

Eberhard Zeidler，德国 Max Planck研究所数学领衔教授，Leipzig大学数学系荣誉教授。曾出版5卷集巨著Nonlinear Functional Analysis & Its Applications（世图已引进出版）。

【目录】

Preface
ContentsofAMSVolume108
1　TheHahn-BanachTheoremOptimizationProblems
1.1TheHahn-BanachTheorem
1.2ApplicationstotheSeparationofConvexSets
1.3TheDualSpaceC[a,b]*
1.4ApplicationstotheMomentProblem
1.5MinimumNormProblemsandDualityTheory
1.6ApplicationstoCebysevApproximation
1.7ApplicationstotheOptimalControlofRockets
2VariationalPrinciplesandWeakConvergence
2.1ThenthVariation
2.2NecessaryandSufficientConditionsforLocalExtremaandtheClassicalCalculusofVariations
2.3TheLackofCompactnessinInfinite-DimensionalBanachSpaces
2.4WeakConvergence
2.5TheGeneralizedWeierstrassExistenceTheorem
2.6ApplicationstotheCalculusofVariations
2.7ApplicationstoNonlinearEigenvalueProblems
2.8ReflexiveBanachSpaces
2.9ApplicationstoConvexMinimumProblemsandVariationalInequalities
2.10ApplicationstoObstacleProblemsinElasticity
2.11SaddlePoints
2.12ApplicationstoDui~lityTheory
2.13ThevonNeumannMinimaxTheoremontheExistenceofSaddlePoints
2.14ApplicationstoGameTheory
2.15TheEkelandPrincipleaboutQuasi-MinimalPoints
2.16ApplicationstoaGeneralMinimumPrincipleviathePalais-SmaleCondition
2.17ApplicationstotheMountainPassTheorem
2.18TheGalerkinMenhodandNonlinearMonotoneOperators
2.19SymmetriesandConservationLaws(TheNoetherTheorem
2.20TheBasicIdeasofGaugeFieldTheory
2.21RepresentationsofLieAlgebras
2.22ApplicationstoElementaryParticles
3PrinciplesofLinearFunctionalAnalysis
3.1TheBaireTheorem
3.2ApplicationtotheExistenceofNondifferentiableContinuousFunctions
3.3TheUniformBoundednessTheorem
3.4ApplicationstoCubatureFormulas
3.5TheOpenMappingTheorem
3.6ProductSpaces
3.7TheClosedGraphTheorem
3.8ApplicationstoFactorSpaces
3.9ApplicationstoDirectSumsandProjections
3.10DualOperators
3.11TheExactnessoftheDualityFunctor
3.12ApplicationstotheClosedRangeTheoremandtoFredholmAlternatives
4TheImplicitFunctionTheorem
4.1m-LinearBoundedOperators
4.2TheDifferentialofOperatorsandtheFr~chetDerivative
4.3ApplicationstoAnalyticOperators
4.4Integration
4.5ApplicationstotheTaylorTheorem
4.6IteratedDerivatives
4.7TheChainRule
4.8TheImplicitFunctionTheorem
4.9ApplicationstoDifferentialEquations
4.10DiffeomorphismsandtheLocalInverseMappingTheorem
4.11EquivalentMapsandtheLinearizationPrinciple
4.12TheLocalNormalFormforNonlinearDoubleSplittingMaps
4.13TheSurjectiveImplicitFunctionTheorem
4.14ApplicationstotheLagrangeMultiplierRule
5FredholmOperators
5.1DualityforLinearCompactOperators
5.2TheRiesz-SchauderTheoryonHilbertSpaces
5.3ApplicationstoIntegralEquations
5.4LinearFredholmOperators
5.5TheRiesz-SchauderTheoryonBanachSpaces
5.6ApplicationstotheSpectrumofLinearCompactOperators
5.7TheParametrix
5.8ApplicationstothePerturbationofFredholmOperators
5.9ApplicationstotheProductIndexTheorem
5.10FredholmAlternativesviaDualPairs
5.11ApplicationstoIntegralEquationsandBoundary-ValueProblems
5.12BifurcationTheory
5.13ApplicationstoNonlinearIntegralEquations
5.14ApplicationstoNonlinearBoundary-ValueProblems
5.15NonlinearFredholmOperators
5.16InterpolationInequalities
5.17ApplicationstotheNavier-StokesEquationsReferences
ListofSymbols
ListofTheorems
ListofMostImportantDefinitions
SubjectIndex