Fourier analysis on coset spaces (Q1288317)

Let \(G\) be a locally compact group with a closed subgroup \(H\). In this paper natural analogs are defined and studied of the Fourier and Fourier-Stieltjes algebras for the homogeneous space \(G/H\) of left cosets of \(H\) in \(G\). In particular, for a compact subgroup \(K\) it is shown that the Fourier algebra \(A(G/K)\) is a regular Banach algebra whose maximal ideal space is \(G/K\), and the amenability of \(G/K\) is characterized in terms of various structural properties of \(A(G/K)\). Moreover, it is proved that \(A(G)\) is weakly amenable for any totally disconnected locally compact group \(G\).