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

9530310 Ehrenpreis该奖项为调和分析在数论和近似理论中的应用会议提供支持。这次会议是为了纪念唐纳德·J·纽曼，会议的重点是受纽曼思想影响的数学领域。这次会议将为古典数学的两个重要领域的工作者创造相互交流思想的机会。数论的历史根源在于对整数的研究，它解决了一些问题，比如一个整数被另一个整数整除的问题。它是数学中最古老的分支之一，出于纯粹的美学原因，人们追寻了许多个世纪。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领域的各种应用中不可或缺的工具。调和分析结合了这些数学元素，最好地例证了综合的思想。一种是试图将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征。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；一个离散的，另一个代表连续的分解。在研究整数时，调和分析是一个令人惊讶的有用工具。

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.