Mathematical Sciences: Topics in Ergodic Theory and OperatorTheory

数学科学：遍历理论和算子理论专题

• 批准号: 9201369
• 负责人: Boris Solomyak
• 金额: $ 4.36万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201369&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Ergodic; Theory

Solomyak will investigate several topics in operator theory related to ergodic theory. The first has connections with K- theory of operator algebras, and centers on the so-called "adic transformations" of Vershik acting on paths of a Bratelli diagram. These transformations define measure-preserving systems whose ergodic and spectral properties will be studied. The proposed approach involves dimension groups, harmonic analysis of measures, and special digit expansions of real numbers. These expansions will be considered in the second part of the project. The third topic concerns the problem of determining the invariant subspace structure for Volterra convolution operators. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

Solomyak将研究算子理论中的几个主题 与遍历理论有关。 第一个与K有关。 算子代数的理论，并集中在所谓的“进 作用于Bratelli路径的Vershik变换 图表。这些变换定义了测度保持系统 其遍历性和谱特性将被研究。 的 所提出的方法涉及维组，谐波分析， 测度和真实的数的特殊数字展开。 这些 将在项目的第二部分考虑扩大。 第三个主题涉及确定不变量的问题 沃尔泰拉卷积算子子空间结构 这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 系统的动力学过于复杂或混乱， 在微观细节上进行跟踪。 在“动态”标题下， 可以把现代理论放在抽象的 变换作用于光滑空间。 这样遍历理论 与几何学接触，以寻求对 齐性空间