If $G$ is a locally compact group, its Fourier-Stieltjes algebra $B(G)$ and its Fourier algebra $A(G)$
were defined by Eymard \cite{Eymard64}. The Fourier-Stieltjes algebra is defined to be the set of coefficient
functions $s \mapsto \pi_{x, y}:=\langle\pi(s) x, y\rangle$ as
$\pi: G \rightarrow$ $B\left(\mathcal{H}_{\pi}\right)$ ranges over the (continuous unitary) representations
of $G$ and $x, y$ over $\mathcal{H}_{\pi}$.

It is well known that $B(G)$ admits a
natural Banach space structure for which it is isometrically isomorphic to the dual
space of the full group $C^*$-algebra $C^*(G)$ associated with $G$.
The Fourier-Stieltjes algebra can be viewed as a subalgebra of $C_{b}(G)$, the Banach algebra of continuous
bounded functions on $G$, and the Fourier
algebra $A(G)$ as an ideal of $B(G)$ contained in $C_{0}(G)$, the $C^{*}$ -algebra of
continuous functions on $G$ which vanish at infinity; for more details see \cite{KaLa18}