Mathematical Sciences: Operator Theory and Noncommutative Harmonic Analysis

数学科学：算子理论和非交换调和分析

• 批准号: 9401380
• 负责人: Hari Bercovici
• 金额: $ 9万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401380&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Theory; Noncommutative

9401380 Bercovici The proposed work is in three directions. The first is in basic operator theory. The theory of dual algebras will be applied to study pairs of commuting operators. These techniques were most successful in the case of single operators. The second direction is related to the study of interpolation and lifting problems associated with the concept of structured singular value. These issues are interesting as problems in operator theory but they also have applications for control theory. The third direction is a development of earlier work in the framework of Voiculescu's free harmonic analysis. The convolution theory in this analysis still has many aspects which are not well understood. For instance, the domain of attraction to the semicircle distribution in the central limit theorem is not known. Problems on large deviations have not been studied in this context. This project lies at the interface of several branches of mathematics (operator theory, probability, function theory). Much of the project involves a better understanding and new results in these disciplines. Further, parts of the project have a significant interaction with control theory and systems theory, and the results might have an impact on calculations related to the control of large systems. ***

9401380 Bercovici拟议的工作是在三个方向上。首先是基本操作者理论。双代数理论将应用于通勤操作员的研究对。在单一操作员的情况下，这些技术最成功。第二个方向与与结构化奇异值概念相关的插值和提升问题的研究有关。这些问题作为操作者理论中的问题很有趣，但它们也具有控制理论的应用。第三个方向是在Voiculescu的自由谐波分析框架内的早期工作的发展。该分析中的卷积理论仍然有许多方面的理解。例如，在中心极限定理中吸引到半圆形分布的吸引域尚不清楚。在这种情况下，尚未研究大偏差的问题。 该项目位于数学几个分支的界面（操作者理论，概率，功能理论）。大部分项目涉及这些学科的更好的理解和新结果。此外，该项目的一部分与控制理论和系统理论具有重要的相互作用，结果可能会影响与大型系统控制有关的计算。 ***