1. Functional analysis [1991]
 Book
 xv, 424 p. ; 24 cm.
 Preface. PART ONE: GENERAL THEORY1. Topological Vector SpaceIntroductionSeparation propertiesLinear MappingsFinitedimensional spacesMetrizationBoundedness and continuitySeminorms and local convexityQuotient spacesExamplesExercises2. CompletenessBaire categoryThe BanachSteinhaus theoremThe open mapping theoremThe closed graph theoremBilinear mappingsExercises3. ConvexityThe HahnBanach theoremsWeak topologiesCompact convex setsVectorvalued integrationHolomorphic functionsExercises4. Duality in Banach SpacesThe normed dual of a normed spaceAdjointsCompact operatorsExercises5. Some ApplicationsA continuity theoremClosed subspaces of LpspacesThe range of a vectorvalued measureA generalized StoneWeierstrass 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 distributionsPaleyWiener 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
(source: Nielsen Book Data)9780070542365 20160528
 Preface. PART ONE: GENERAL THEORY1. Topological Vector SpaceIntroductionSeparation propertiesLinear MappingsFinitedimensional spacesMetrizationBoundedness and continuitySeminorms and local convexityQuotient spacesExamplesExercises2. CompletenessBaire categoryThe BanachSteinhaus theoremThe open mapping theoremThe closed graph theoremBilinear mappingsExercises3. ConvexityThe HahnBanach theoremsWeak topologiesCompact convex setsVectorvalued integrationHolomorphic functionsExercises4. Duality in Banach SpacesThe normed dual of a normed spaceAdjointsCompact operatorsExercises5. Some ApplicationsA continuity theoremClosed subspaces of LpspacesThe range of a vectorvalued measureA generalized StoneWeierstrass 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 distributionsPaleyWiener 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
(source: Nielsen Book Data)9780070542365 20160528
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA320 .R83 1991  Unknown On reserve at Li and Ma Science Library 2hour loan 
QA320 .R83 1991  Unknown On reserve at Li and Ma Science Library 2hour loan 
MATH27101
 Course
 MATH27101  The HPrinciple
 Instructor(s)
 Luk, Jonathan Winghong
2. Methods of modern mathematical physics [1980  ]
 Book
 v. : ill. ; 24 cm.
 v. 1. Functional analysis.
(source: Nielsen Book Data)9780125850506 20160528
 v. 1. Functional analysis.
(source: Nielsen Book Data)9780125850506 20160528
SAL3 (offcampus storage), Science Library (Li and Ma)
SAL3 (offcampus storage)  Status 

Science Library (Li and Ma)  Status 

Stacks


QC20.7 .F84 R43 1980 V.1  Unknown On reserve at Li and Ma Science Library 2hour loan 
QC20.7 .F84 R43 1980 V.1  Unknown On reserve at Li and Ma Science Library 2hour loan 
MATH27101
 Course
 MATH27101  The HPrinciple
 Instructor(s)
 Luk, Jonathan Winghong