| 作者简介 Professor Deitmar holds a Chair in Pure Mathematics at the University of Exeter, U.K. He is a former Heisenberg fellow and was awarded the main prize of the Japanese Association of Mathematical Sciences in 1998. In his leisure time he enjoys hiking in the mountains and practicing Aikido. |
| Ⅰ Fourier Analysis 1 Fourier Series 1.1 Periodic Functions 1.2 Exponentials 1.3 The Bessel Inequality 1.4 Convergence in the L2-Norm 1.5 Uniform Convergence of Fourier Series 1.6 Periodic Functions Revisited 1.7 Exercises 2 Hilbert Spaces 2.1 Pre-Hilbert and Hilbert Spaces 2.2 l2-Spaces 2.3 Orthonormal Bases and Completion 2.4 Fourier Series Revisited 2.5 Exercises 3 The Fourier Transform 3.1 Convergence Theorems 3.2 Convolution 3.3 The Transform 3.4 The Inversion Formula 3.5 Plancherel's Theorem 3.6 The Poisson Summation Formula 3.7 Theta Series 3.8 Exercises 4 Distributions 4.1 Definition 4.2 The Derivative of a Distribution 4.3 Tempered Distributions 4.4 Fourier Transform 4.5 Exercises Ⅱ LCA Groups 5 Finite Abelian Groups 5.1 The Dual Group 5.2 The Fourier Transform 5.3 Convolution 5.4 Exercises 6 LCA Groups 6.1 Metric Spaces and Topology 6.2 Completion 6.3 LCA Groups 6.4 Exercises 7 The Dual Group 7.1 The Dual as LCA Group …… 8 Plancherel Theorem Ⅲ Noncommutative Groups 10 The Representations of SU（2） 11 The Peter -Weyl Theorem 12 .The Heisenberg Group A The Riemann Zeta Function B Haar Integration Bibiliography Index |
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