华章数学原版精品系列泛函分析(英文版.原书第2版.典藏版) 内容简介

CONTENTSPrefaceAbout thd AuthorPart I General TheoryTopological Vector SpacesIntroductionSeparation propertiesLinear mappingsFinite-dimensional spacesMetrizationBoundedness and continuitySeminorms and local convexityQuotient spacesExamplesExercises2 CompletenessBaire categoryThe Banach-Steinhaus theoremThe open mapping theoremThe closed graph theoremBilinear mappingsExercises3 ConvexityThe Hahn-Banach theoremsWeak topologiesCompact convex setsVector-valued integrationHolomorphic functionsExercises4 Duality in Banach SpacesThe normed dual of a normed spaceAdjointsCompact operatorsExercises5 Some ApplicationsA continuity theoremClosed subspaces of fi-spacesThe range of a vector-valued measureA generalized Stone-Weierstrass theoremTwo interpolation theoremsKakutani''''s fixed point theoremHaar measure on compact groupsUncomplemented subspacesSums of Poisson kernelsTwo more fixed point theoremsExercisesPart II Distributions and Fourier Transform6 Test Functions and DistributionsIntroductionTest function spacesCalculus with distributionsLocalizationSupports of distributionsDistributions as derivativesConvolutionsExercises7 Fourier TransformsBasic propertiesTempered d]str]but]onsPaley-Wiener theoremsSobolev''''s lemmaExercises8 Applications to Differential EquationsFundamental solutionsElliptic equationsExercises9 Tauberian TheoryWiener''''s theoremThe prime number theoremThe renewal equationExercisesPart III Banach Algebras and Spectral Theory10 Banach AlgebrasIntroductionComplex homomorphismsBasic properties of spectraSymbolic calculusThe group of invertible elementsLomonosov''''s invariant subspace theoremExercises11 Commutative Banach AlgebrasIdeals and homomorphismsGelfand transformsInvolutionsApplications to noncommutative algebrasPositive functionalsExercises12 Bounded Operators on a Hilbert SpaceBasic factsBounded operatorsA commutativity theoremResolutions of the identityThe spectral theoremEigenvalues of normal operatorsPositive operators and square rootsThe group of invertible operatorsA characterization of B*-algebrasAn ergodic theoremExercises13 Unbounded OperatorsIntroductionGraphs and symmetric operatorsThe Cayley transformResolutions of the identityThe spectral theoremSemigroups of operatorsExercisesAppendix A Compactness and ContinuityAppendix B Notes and CommentsBibliographyList of Spe SymbolsIndex

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