Banach algebras in abstract harmonic analysis

抽象调和分析中的巴纳赫代数

• 批准号: RGPIN-2015-05044
• 负责人: Stokke, Ross
• 金额: $ 0.8万
• 依托单位: University of Winnipeg
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635276
• 关键词: Banach; algebras; abstract; harmonic; analysis

This proposal lies in the area of abstract harmonic analysis, which is largely the study of locally compact (topological) groups and their associated Banach algebras. Locally compact groups are abstract mathematical objects, which may be associated with the symmetries of a geometric figure, or the rigid motion of objects in nature. They have many applications, both to the mathematical and physical sciences. A Banach algebra is a collection of elements such that each individual element has a length, and such that any two elements can be added or multiplied. These Banach algebras are often comprised of mappings into the set of real, or complex, numbers, and they are also often comprised of operators, which may be viewed as finite, or infinite, arrays of numbers. There are many interesting and useful Banach algebras naturally associated with any locally compact group, and a general theme in this area of research is to study the relationship between various properties of locally compact groups and their associated Banach algebras. In many ways, this theme is prominent in this research program.

这一建议属于抽象调和分析领域，这主要是研究局部紧（拓扑）群及其相关的巴拿赫代数。局部紧群是抽象的数学对象，它可能与几何图形的对称性或自然界中物体的刚性运动有关。它们在数学和物理科学中都有很多应用。巴拿赫代数是元素的集合，这样每个单独的元素都有一个长度，并且任何两个元素都可以相加或相乘。这些Banach代数通常由实数或复数集合的映射组成，它们也通常由运算符组成，这些运算符可以被视为有限或无限的数字数组。有许多有趣和有用的Banach代数自然地与任何局部紧群相关联，而这一研究领域的一般主题是研究局部紧群的各种性质与它们所关联的Banach代数之间的关系。在很多方面，这个主题在这个研究项目中都很突出。