Mathematical Sciences: Problems in Trigonometric Series and Applications

在这个项目中，主要研究人员将在傅立叶分析中的一些有趣的问题上单独和共同工作。要考虑的具体问题包括：正交函数系的重排，高维Besicovitch集的度量性质及其与傅立叶级数的Bochner-Riesz可和性的关系，以及Dirichlet和的分布性质。这些主题中的每一个在经典分析中都有悠久的历史，主要的研究人员站在数学家的前列，致力于提高我们对傅立叶级数的理解。傅里叶级数出现在许多纯粹的和应用的背景下，可以毫不夸张地说，他们的研究为20世纪的分析提供了很大的动力。这个项目的主要研究人员是当今世界上最伟大的两位分析家，他们建议研究一些关于傅里叶级数的性质和由它们定义的函数的挑战性问题。

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.