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.

本文的研究内容涉及算子及其不变子空间的研究，以及自由随机变量理论中的一些问题。 不变子空间的问题将集中在结构和分类的结果，在特殊情况下，可以推断出从组合学的杨表。 自由概率中的问题将涉及任意阵列的弱律，以及乘法稳定性的研究。 自由卷积的精细调和分析也将被研究。这里提出的工作主要是理论性质的，它旨在澄清不同领域（如算子理论，复分析和组合分析）研究对象之间的一些（有时是意想不到的）联系。 这种工作通常与更多的应用领域有联系。 与算子理论密切相关的一个具体应用领域是控制理论和最优化，算子在这些领域确实有着相当惊人的应用。