Banach algebras in abstract harmonic analysis

这一建议是在该地区的抽象调和分析，这主要是研究局部紧（拓扑）群及其相关的Banach代数。局部紧群是抽象的数学对象，它可以与几何图形的对称性或自然界中物体的刚性运动相联系。它们在数学和物理科学中都有许多应用。Banach代数是一个元素的集合，每个元素都有一个长度，并且任何两个元素都可以相加或相乘。 这些Banach代数通常由映射到真实的或复数的集合组成，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，并且在这一研究领域的一般主题是研究局部紧群的各种性质与其相关联的Banach代数之间的关系。在许多方面，这个主题在这个研究计划中很突出。

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.