Operator Theory, Free Harmonic Analysis, and Related Problems

算子理论、自由谐波分析及相关问题

• 批准号: 0070459
• 负责人: Hari Bercovici
• 金额: $ 11.55万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070459&HistoricalAwards=false
• 关键词: Operator; Theory; Free; Harmonic; Analysis

ABSTRACTDMS-0070459The proposed research involves the study of operators and their invariantsubspaces, and some problems arising in the theory of free random variables. The problems on invariant subspaces will focus on the structure andclassification results which can in special cases be inferred from the combinatorics ofYoung tableaux. Problems in free probability will concern the weak lawsfor arbitrary arrays, and the study of multiplicative stability. Thefiner harmonic analysis of free convolutions will also be studied.The work proposed here is mostly of a theoretical nature, and it isintended to clarify some (sometimes unexpected) connections between objects studiedin different areas (such as operator theory, complex analysis, andcombinatorial analysis). This kind of work does often have connectionswith more applied areas. The one specific applied area closely related to the operator theoryis control theory and optimization where operators have indeed found rather strikingapplications.

AbstractDMS-0070459拟议的研究涉及对操作员及其不变式面积的研究，以及在自由随机变量理论中引起的一些问题。 不变子空间上的问题将集中在结构和分类结果上，在特殊情况下可以从Young tableaux的组合学中推断出来。 自由概率的问题将涉及薄弱的任意阵列的法律以及对乘法稳定性的研究。 此处提出的作品主要是理论性质，因此，对自由卷积的谐波分析也将阐明研究中研究的对象之间（例如操作员理论，复杂分析，复杂分析和combinatorial分析）之间的某些（有时是意外的）连接。 这种工作通常与更多应用领域具有连接。 一个特定的应用领域与操作者理论控制理论和优化相关的一个特定的应用领域确实发现了相当引人注目的应用程序。