Mathematical Sciences: Problems in Trigonometric Series and Applications

数学科学：三角级数问题及其应用

• 批准号: 9107476
• 负责人: Jean Bourgain
• 金额: $ 3.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-15 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107476&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Trigonometric; Series

In this project the principal investigators will work separately and jointly on a number of interesting problems in Fourier Analysis. Among the specific topics to be considered are the following: rearrangements of orthogonal systems of functions, the metrical properties of Besicovitch sets in higher dimensions and their relationship to the Bochner-Riesz summability of Fourier series, and the distributional properties of Dirichlet sums. Each of these topics has a long and venerable history in classical analysis, and the principal investigators are in the forefront of mathematicians working on improving our understanding of Fourier series. Fourier series arise in a host of pure and applied contexts, and it is not an exaggeration to say that their study has provided much of the motivation for twentieth-century analysis. The principal investigators in this project are two of the greatest analysts in the world today, and they propose to study some challenging questions regarding the properties of Fourier series and the functions defined by them.

在这个项目中，主要研究人员将 单独和共同就一些有趣的问题， 傅立叶分析 需要考虑的具体议题包括 以下：正交系统的重排 函数，贝西科维奇集的度量性质在较高的 尺寸及其与Bochner-Riesz的关系 傅里叶级数的可和性和分布性质 Dirichlet Sums的 这些主题中的每一个都有一个漫长而古老的 古典分析中的历史，以及主要研究者 都站在数学家的最前沿， 了解Fourier级数。 傅立叶级数出现在许多纯粹的和应用的背景下， 毫不夸张地说，他们的研究 为20世纪的分析提供了很大的动力。 该项目的主要研究人员是 当今世界最伟大的分析师，他们建议研究 关于傅立叶性质的一些挑战性问题 系列及其定义的功能。