Mathematical Sciences: Conference on Harmonic Analysis to Honor Donald J. Newman; March 11-14, 1996; Philadelphia, PA.

数学科学：调和分析会议以纪念唐纳德·J·纽曼；

• 批准号: 9530310
• 负责人: Leon Ehrenpreis
• 金额: $ 1.2万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-03-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9530310&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Conference; Harmonic; Analysis

9530310 Ehrenpreis This award provides support for a conference on applications of harmonic analysis in number theory and approximation theory. The conference is being held in honor of Donald J. Newman, and the emphasis is on areas of mathematics that have been influenced by Newman's ideas. The conference will create opportunities for cross-fertilization of ideas among workers in two important areas of classical mathematics. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems. Harmonic analysis combines those elements of mathematics best exemplifying the ideas of synthesis. One seeks to decompose complex problems into fundamental components. These components are then analyzed for their basic characteristics. Finally, the solution is reconstructed through a recombination of the components.The Fourier series and Fourier transform are examples of tools used in this context; one discrete , the other representing a continuous decomposition. Harmonic analysis is a surprisingly useful tool in studying whole numbers.

这个奖项为一个关于调和分析在数论和近似理论中的应用的会议提供支持。这次会议是为了纪念唐纳德·j·纽曼而举行的，重点是受纽曼思想影响的数学领域。这次会议将为经典数学两个重要领域的工作者之间的思想交流创造机会。数论的历史根源在于对整数的研究，解决的问题是一个整数能被另一个整数整除的问题。它是数学中最古老的分支之一，人们为了纯粹的美学原因而追求了许多世纪。然而，在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等各种应用领域不可或缺的工具。谐波分析结合了最能体现综合思想的数学元素。人们试图把复杂的问题分解成基本的组成部分。然后分析这些组件的基本特性。最后，通过组件的重组重构解。傅里叶级数和傅里叶变换是在这种情况下使用的工具的例子；一个是离散的，另一个是连续的。谐波分析在研究整数时是一个非常有用的工具。