Preface 1 Banach Algebras and Spectral Theory 1.1 Banach Algebras：Basic Concepts 1.2 Gelfand Theory 1.3 Nonunital Banach Algebras 1.4 The Spectral Theorem 1.5 Spectral Theory of Representations 1.6 Von Neumann Algebras 1.7 Notes and References 2 Locally Compact Groups 2.1 Topological Groups 2.2 Haar Measure 2.3 Interlude：Some Technicalities 2.4 The Modular Function 2.5 Convolutions 2.6 Homogeneous Spaces 2.7 Notes and References 3 Basic Representation Theory 3.1 Unitary Representations 3.2 Representations of a Group and Its Group Algebra 3.3 Functions of Positive Type 3.4 Notes and References 4 Analysis on Locally Compact Abelian Groups 4.1 The Dual Group 4.2 The Fourier Transform 4.3 The Pontrjagin Duality Theorem 4.4 Representations of Locally Compact Abelian Groups 4.5 C!losed Ideals in LG 4.6 Spectral Synthesis 4.7 The Bohr Compactification 4.8 Notes and References 5 Analysis on Compact Groups 5.1 Representations of Compact Groups 5.2 The Peter.Weyl Theorem 5.3 Fourier Analysis on Compact Groups 5.4 Examples 5.5 Notes and Rfeferences 6 Induced Representations 6.1 The Inducing Construction 6.2 The Frobenius Reciprocity Theorem 6.3 Pseudomeasures and Induction in Stages 6.4 Systems of Imprimitivity 6.5 The Imprimitivity Theorem 6.6 Introduction to the Mackey Machine 6.7 Examples：The Classics 6.8 More Examples，Good and Bad 6.9 Notes and References 7 Further Topics in Representation Theory 7.1 The Group Calgebra 7.2 The Structure of the Dual Space
7.3 Tensor Products of Representations 7.4 Direct Integral Decompositions 7.5 The Plancherel Theorem 7.6 Examples Appendices 1 A Hilbert Space Miscellany 2 Nace-Class and Hilbert.Schmidt Operators 3 Tensor Products of Hilbert Spaces 4 Vector—Valued Integrals Bibliography Index
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