Stein在国际上享有盛誉,现任美国普林斯顿大学数学系教授。
他是当代分析,特别是调和分析和分析领域领袖人物之一。古典调和分析最困难问题之一是推广到多维。他是多维欧氏调和分析的创造者之一,为此他发展了许多先进工具如奇异积分、Radon变换、极大函数等。他还发展了多个实变元的Hardy空间理论,推广了1971年F. John和L. Nirenberg的重要发现:即Hardy空间与BMO空间的对偶。在群上的调和分析方面也有贡献,例如同R.Kunze一起发现所谓Kunze-Stein现象。除此之外,他对多复变问题也做出了突出成绩。
除了研究工作之外,他的许多书成为影响学科发展的重要参考文献。为此,他荣获1984年美国数学会在论述方面的Steele奖。
由于他的成就,他在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,1993年获得瑞士科学院颁发的Schock奖。1999年获得世界性Wolf数学奖。
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences - that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. "The Princeton Lectures in Analysis" represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which "Fourier Analysis" is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing "Fourier" series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
快要高考了,但最近还是抽时间看了本书电子书的前五章,加上之前看过Singer和Thorope的《讲义》和Spanier的《代数拓扑》,三本英文书应该不算很多吧,但是它们给我一个明显的感觉就是我们的教材太单薄了,用Zorich的话来说,我们的教科书只剩下一个个的定理和论证(诚实地讲,...
评分http://bbs.whu.edu.cn/wForum/boardcon.php?bid=41&id=7392&ftype=0 一开始从历史的角度引出傅立叶级数,举了两个例子,弦振动和热方程。如果学过偏微的 话算是复习了。如果没学过也无所谓,里面的推导具体详实,不会有理解上的问题。 傅立叶级数是否会收敛到原函数?后面...
评分快要高考了,但最近还是抽时间看了本书电子书的前五章,加上之前看过Singer和Thorope的《讲义》和Spanier的《代数拓扑》,三本英文书应该不算很多吧,但是它们给我一个明显的感觉就是我们的教材太单薄了,用Zorich的话来说,我们的教科书只剩下一个个的定理和论证(诚实地讲,...
评分作为一个物理系的学生,这本书的内容可以说是很适合学物理来观摩观摩!大师Stein用分析学的方法深入浅出地介绍并引导出fourier series和fourier transformation,并且大量介绍了fourier analysis在物理与数学中的应用。 当然,人家讲得精彩的同时,留的习题也是相当精彩的,习...
看的很开心
评分学完大一课程就能读的一本书,让我明白了分析作为工具的强大之处
评分什么时候再捡起来把后面几章读完…
评分最后一章Dirichlet theorem 没能耐心读完,习题做的也比较少,有机会还得再过一边,难得一见的好书
评分看的很开心
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