Group orbits in garmonic analysis and ergodic theory.

调和分析和遍历理论中的群轨道。

• 批准号: ARC : DP0210021
• 负责人: Prof Anthony Dooley
• 金额: $ 46.5万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2002
• 资助国家: 澳大利亚
• 起止时间: 2002-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/group-orbits-garmonic-ergodic-theory/72731
• 关键词: Group; orbits; garmonic; analysis; ergodic

Group orbits in garmonic analysis and ergodic theory. Researchers from many areas need a type of mathematical analysis which involves the behaviour of a system - which may be a set of data points - under repeated application of some operation or group of operations. The structures arising from this kind of process are known as group orbits. The project gives information about their nature. Two major types of orbits are considered, coming from actions of discrete groups on measure spaces, and from smooth actions of Lie groups on manifolds, where powerful geometric methods are available. The project will yield new understandings of entropy, and new approaches to Fourier analysis.

群轨道在Garmonic分析和遍历理论中的应用。来自许多领域的研究人员需要一种数学分析，这种分析涉及系统的行为-可能是一组数据点-在重复应用某些操作或一组操作的情况下。这种过程产生的结构称为群轨道。该项目提供了有关其性质的信息。两种主要类型的轨道被认为是，来自行动的离散群的措施空间，并从光滑行动的李群流形上，强大的几何方法。该项目将产生熵的新理解，以及傅立叶分析的新方法。