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| 作者作为数学界的大师，将傅立叶变换的各个方面用浅显的语言呈现给读者。国内的相关书籍大多要么晦涩难懂，要么需要相当多的相关知识，要么覆盖面不广。而这本书籍很好的解决了这些问题，并且和后续的复变函数、实变分析相互照应，使人受益匪浅。 |
| 作者Stein在国际上享有盛誉,1现任美国普林斯顿大学数学系教授,1是当代分析,1特别是调和分析领域领袖人物之一.a1974年被选为美国国家科学院院士,11982年被选为美国文理学院院士,11984年获美国数学会的Steele奖,11993年获得瑞士科学院颁发的Schock奖,11999年获得世界性Wolf数学奖. |
| Foreword Preface Chapter 1. The Genesis of Fourier Analysis 1 The vibrating string 2 The heat equation 3 Exercises 4 Problem Chapter 2. Basic Properties of Fourier Series 1 Examples and formulation of the problem 2 Uniqueness of Fourier series 3 Convolutions 4 Good kernels 5 Cesaro and Abel summability：applications to Fourier series 6 Exercises 7 Problem Chapter 3. Covergence of Fourier Series 1 Mean-square convergence of Fourier Series 2 Return to Pointwise Convergence 3 Exercises 4 Problem Chapter 4. Some Applications of Fourier Series 1 The isoperimetric inequality 2 Weyl's equidistribution theorem 3 A Continuous but nowhere differentiable function 4 The heat equation on the circle 5 Exercises 7 Problems Chapter 5. The Fourier Transform on R 1 Elementary theory of the Fourier transform 2 Applictions to some partial differential equations 3 The poisson summation formula 4 The Heisenberg uncertainty principle 5 Exercises 6 Problems Chapter 6. The Fourier Transform on Rd 1 Preliminaries 2 Elementary of the Fourier transform 3 The wave equation in Rd×R …… Chapter 7 Finite Fourier Analysis Chapter 8 Dirichlet's Theorem Appendix: Integration Notes and References Bibliography Symbol Glossary |
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