Homomorphisms, representations and amenability of group and Fourier algebras on locally compact groups

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。对于任何局部紧群，可以将几个有用的映射集合关联到实数或复数集合中。操作符可以被解释为有限或无限的数字数组，并且还有许多与这些局部紧群相关的操作符集合。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。上述的函数集合和算子集合都是Banach代数的例子，本文研究了这些Banach代数的各种性质与它们底层的局部紧群的性质之间的关系。

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. With any locally compact group, one can associate several useful collections of mappings into the set of real, or complex, numbers. An operator may be interpreted as a finite or infinite array of numbers, and there are also many relevant collections of operators associated to these locally compact groups. 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. The aforementioned collections of functions and collections of operators are examples of Banach algebras, and this proposal is concerned with the study of various properties of these Banach algebras in relation to properties of their underlying locally compact groups.