Mathematical Sciences: The Norbert Wiener Centenary Congress;East Lansing, Michigan; November 27-December 3, 1994

数学科学：诺伯特·维纳百年大会；密歇根州东兰辛；

• 批准号: 9411399
• 负责人: V. Mandrekar
• 金额: $ 2.04万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-15 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9411399&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Norbert; Wiener; Centenary

9411399 Mandrekar The objective of the Congress is to recall the legacy of Norbert Wiener and record its continuation in ongoing research. The legacy comprises first the idealization of Einstein's theory of Brownian motion. Wiener's work in this context constitutes the foundation of the stochastic integration, stochastic differential equations, and integration on infinite-dimensional spaces.. These three major fields in probability have significant applications to engineering, control theory, finance, and quantum physics. The legacy also includes Wiener's work on generalized harmonic analysis, which has had numerous ramifications, the most recent being the theory of wavelets, which in turn is being used in the statistical application for the storage of data. In addition, the legacy comprises the notions of capacity and generalized solution of the Dirichlet problem, which in the 1990's has received a beautiful extension to nonlinear PDE's of order p 1. Probabilistic ideas of Norbert Wiener have led to the solu ions of fundamental problems of Potential Theory and Harmonic Analysis. These areas are being actively pursued today and the Congress will strive to inspire young probabilists and analysts to continue Wiener's work in his innovative way.

会议的目的是回顾诺伯特·维纳的遗产，并记录其在正在进行的研究中的延续。遗产首先包括爱因斯坦的布朗运动理论的理想化。维纳在这方面的工作构成了随机积分、随机微分方程和无限维空间上的积分的基础。概率论的这三个主要领域在工程、控制理论、金融和量子物理中都有重要的应用。遗产还包括维纳在广义谐波分析方面的工作，该工作产生了许多分支，最近的是小波理论，而小波理论又被用于数据存储的统计应用。此外，该遗产还包括Dirichlet问题的容量和广义解的概念，该问题在20世纪90年代得到了对p阶非线性偏微分方程的漂亮扩展。诺贝特·维纳的概率思想导致了势理论和谐波分析基本问题的解决。今天，这些领域正在得到积极的研究，大会将努力激励年轻的概率学家和分析师以维纳的创新方式继续他的工作。