MMath Research Project Presentation

John Sawatzky, Department of Pure Mathematics, University of Waterloo

"Fourier algebras"

For a given locally compact group G, we will discuss the space of matrix coefficients associated with the left regular representation. This space is known as the Fourier Algebra A(G), and is actually a closed ideal inside the Fourier-Stieltjes algebra B(G). We will look at a number of interesting properties of A(G), such as the fact that its spectrum is just G itself, that A(G) has a bounded approximate identity if and only if G is amenable, and that if H is a closed subgroup of G then A(G)|_H = A(G).

MC 5417