NSF/CBMS Regional Conference in the Mathematical Sciences: Wave Packets, Multilinear Operators and Carleson Theorems; May 23-28, 2004; Atlanta, GA

NSF/CBMS 数学科学区域会议：波包、多线性算子和卡尔森定理；

• 批准号: 0332476
• 负责人: Gerd Mockenhaupt
• 金额: $ 3.2万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-05-01 至 2005-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0332476&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

The subject area is in the area of multilinear singular integrals, and some related maximal operators, with a particular emphasis on those with some invariance properties with respect to modulations. This is a new branch of Harmonic Analysis that has arisen within the last decade.A distinguishing feature of this area is the use of wave packet techniques which have roots going back to seminal work on convergence of Fourier series by L. Carleson, and C. Fefferman about 40 years ago. Yet the use of these techniques was hardly felt outside the subject of convergence of Fourier series until 1995. It was then that M. Lacey and C. Thiele used related techniques to a long standing conjecture of A. Calderon concerning the bilinear Hilbert transform.It is now understood, through the efforts of a sizable number of mathematicans, that these techniques are crucial to the study a wide class of multilinear singular integral and maximal operators. The timing of these lectures occurs when there is already a body of sophisticated results, from which are emerging signs of a beautiful theory. Connections to other fields of mathematics are at the horizon.Professor Thiele's will present this recent development in a series of lectures and there will be a few additional lectures by leading researchers in the subject.

该主题领域位于多线性奇异积分和一些相关的最大算子的区域，特别强调了与调制有关的具有某些不变特性的人。 这是一个新的谐波分析分支，它在过去十年中已经出现了。该领域的区别特征是使用波数据包技术，其根源可以追溯到L. Carleson的傅立叶系列收敛性工作，而C. Fefferman大约40年前。然而，直到1995年，几乎没有感觉到这些技术的使用几乎没有被感觉到。直到1995年。那时，莱西（M. Lacey）和C. thiele使用相关的技术来实现A. calderon的长期猜想。最大操作员。这些讲座的时机发生在已经有一个复杂的结果时，这是一个美丽的理论的新兴迹象。 与其他数学领域的联系处于地平线上。蒂尔（Thiele）将在一系列讲座中介绍这一最新发展，并将在该主题中领先的研究人员进行一些其他讲座。