  We give a characterisation of radial Schur multipliers on finite products of
trees. The equivalent condition is that a certain generalised Hankel matrix
involving the discrete derivatives of the radial function is a trace class
operator. This extends Haagerup, Steenstrup and Szwarc's result for trees. The
same condition can be expressed in terms of Besov spaces on the torus. We also
prove a similar result for products of hyperbolic graphs and provide a
sufficient condition for a function to define a radial Schur multiplier on a
finite dimensional CAT(0) cube complex.
