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xv, 424 p. ; 24 cm.
  • Preface. PART ONE: GENERAL THEORY1. Topological Vector SpaceIntroductionSeparation 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 Lp-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 TWO: DISTRIBUTIONS AND FOURIER TRANSFORMS6. Test Functions and DistributionsIntroductionTest function spacesCalculus with distributionsLocalizationSupports of distributionsDistributions as derivativesConvolutionsExercises7. Fourier TransformsBasic propertiesTempered distributionsPaley-Wiener theoremsSobolev's lemmaExercises8. Applications to Differential EquationsFundamental solutionsElliptic equationsExercises9. Tauberian TheoryWiener's theoremThe prime number theoremThe renewal equationExercisesPART THREE: 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 Hillbert 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 Special SymbolsIndex.
  • (source: Nielsen Book Data)9780070542365 20160528
This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
(source: Nielsen Book Data)9780070542365 20160528
Science Library (Li and Ma)
v. : ill. ; 24 cm.
  • v. 1. Functional analysis.
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
(source: Nielsen Book Data)9780125850506 20160528
SAL3 (off-campus storage), Science Library (Li and Ma)