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目次

Banach Algebras and Spectral TheoryBanach Algebras: Basic ConceptsGelfand TheoryNonunital Banach AlgebrasThe Spectral TheoremSpectral Theory of *-RepresentationsNotes and ReferencesLocally Compact GroupsTopological GroupsHaar MeasureInterlude: Some TechnicalitiesThe Modular FunctionConvolutionsHomogeneous SpacesNotes and ReferencesBasic Representation TheoryUnitary RepresentationsRepresentations of a Group and its Group AlgebraFunctions of Positive TypeNotes and ReferencesAnalysis on Locally Compact Abelian GroupsThe Dual GroupThe Fourier TransformThe Pontrjagin Duality TheoremRepresentations of Locally Compact Abelian GroupsClosed Ideals in L1(G)Spectral SynthesisThe Bohr CompactificationNotes and ReferencesAnalysis on Compact GroupsRepresentations of Compact GroupsThe Peter-Weyl TheoremThe Fourier Transform on Compact GroupsExamplesNotes and ReferencesInduced RepresentationsThe Inducing ConstructionThe Frobenius Reciprocity TheoremPseudomeasures and Induction in StagesSystems of ImprimitivityThe Imprimitivity TheoremIntroduction to the Mackey MachineExamplesNotes and ReferencesFurther Topics in Representation TheoryThe Group C* AlgebraThe Structure of the Dual SpaceTensor ProductsDirect Integral DecompositionsThe Plancherel TheoremExamplesAppendix 1. Hilbert Space MiscellanyAppendix 2. Trace-Class and Hilbert-Schmidt OperatorsAppendix 3. Vector-Valued IntegralsBibliographyIndex