傅立叶分析导论(数学经典英文教材系列)
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品牌: Elias M.Stein、Rami Shakarchi
基本信息·出版社：世界图书出版公司
·页码：311 页
·出版日期：2006年
·ISBN：7506272873
·条形码：9787506272872
·包装版本：第1版
·装帧：平装
·开本：24开
·丛书名：数学经典英文教材系列
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内容简介《傅立叶分析导论》分为3部分：第1部分介绍傅立叶级数的基本理论及其在等周不等式和等分布中的应用；第2部分研究傅立叶变换及其在经典偏微分方程及Radom变换中的应用；第3部分研究有限阿贝尔群上的傅立叶分析。书中各章均有练习题及思考题。
作者简介作者Stein在国际上享有盛誉，现任美国普林斯顿大学数学系教授，是当代分析，特别是调和分析领域领袖人物之一。1974年被选为美国国家科学院院士，1982年被选为美国文理学院院士，1984年获美国数学会的Steele奖，1993年获得瑞士科学院颁发的Stchock奖，1999年获得世界性Wolf数学奖。
编辑推荐《傅立叶分析导论》由在国际上享有盛誉的普林斯顿大学教授Stein撰写而成，是一部傅立叶分析的入门教材，理论与实践并重。为了便于非数学专业的学生学习，全书内容简明、易懂。
目录
Foreword PrefaceChapter 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 ProblemChapter 3. Covergence of Fourier Series1 Mean-square convergence of Fourier Series2 Return to Pointwise Convergence3 Exercises 4 ProblemChapter 4. Some Applications of Fourier Series1 The isoperimetric inequality2 Weyl's equidistribution theorem3 A Continuous but nowhere differentiable function4 The heat equation on the circle5 Exercises7 ProblemsChapter 5. The Fourier Transform on R1 Elementary theory of the Fourier transform2 Applictions to some partial differential equations3 The poisson summation formula4 The Heisenberg uncertainty principle5 Exercises6 ProblemsChapter 6. The Fourier Transform on Rd1 Preliminaries2 Elementary of the Fourier transform3 The wave equation in Rd×R……Chapter 7 Finite Fourier AnalysisChapter 8 Dirichlet's TheoremAppendix: IntegrationNotes and ReferencesBibliographySymbol Glossary
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序言Any effort to present an overall view of analysis must at its start deal with the following questions: Where does one begin? What are the initial subjects to be treated, and in what order are the relevant concepts and basic techniques to be developed? . Our answers to these questions are guided by our view of the centrality of Fourier analysis, both in the role it has played in the development of the subject, and in the fact that its ideas permeate much of the presentday analysis. For these reasons we ]lave devoted this first volume to an.
