A Characterization of Radial Herz-Schur Multipliers on Free Products of Discrete Groups

A characterization of radial Herz-Schur multipliers on groups which are free products G = ∗Ni=1Gi of subgroups of the same order (finite or infinite) is given. The multiplier norm is computed in terms of trace norms of appropriate trace operators. This applies in particular to free groups FN = ∗Ni=1 Z with block length. This method also applies to characterizing radial multipliers of free product groups of distinct orders, all greater than 2, but in this case we can compute only the multiplier norm up to some constant.