$L^{p}$-convolution operators supported by subgroups

Abstract:

Let G be a compact nonabelian group and H be a closed subgroup of G. Then H is a set of spectral synthesis for the Fourier algebra $A(G)$ (and indeed for ${A^p}(G),1 \leqq p < \infty$). For $1 \leqq p < \infty$, each ${L^p}(G)$-multiplier T corresponds to a ${L^p}(H)$-multiplier S by the rule $(Tf)|H = S(f|H),f \in A(G)$, if and only if the support of T is contained in H.