Algebras of abstract harmonic analysis

抽象调和分析的代数

• 批准号: RGPIN-2015-04024
• 负责人: Spronk, Nicolaas
• 金额: $ 1.02万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=589544
• 关键词: Algebras; abstract; harmonic; analysis

The mathematical concept of a group is the most basic expression of symmetry. An object like a square admits only finitely many symmetries, whereas a sphere or plane admits infinitely many. In order to keep the analysis of such a group of symmetries more tractable, and to remember more of the spatial features of the underlying sphere or plane, say, one needs to deal with the spatial properties of the symmetry group, a concept we call topology. Hence we obtain topological groups. Furthermore, most natural examples, such as those above, suggest a certain finiteness near individual points, a condition we call local compactness.

群的数学概念是对称性的最基本表达。 像正方形这样的物体只允许有200多种对称性，而球面或平面则允许有无限多种对称性。 为了使对这样一组对称性的分析更容易处理，并记住更多的基础球面或平面的空间特征，比如说，我们需要处理对称性群的空间性质，我们称之为拓扑学。 因此，我们得到拓扑群。 此外，大多数自然的例子，比如上面的例子，暗示了在单个点附近的某种有限性，我们称之为局部紧性。