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We investigate the dispersive properties of solutions to the Schr\"odingerequation with a weakly decaying radial potential on cones. If the potential hassufficient polynomial decay at infinity, then we show that the Schr\"odingerflow on each eigenspace of the link manifold satisfies a weighted $L^1\toL^\infty$ dispersive estimate. In odd dimensions, the decay rate we compute isconsistent with that of the Schr\"odinger equation in a Euclidean space of thesame dimension, but the spatial weights reflect the more complicated regularityissues in frequency that we face in the form of the spectral measure. In evendimensions, we prove a similar estimate, but with a loss of $t^{1/2}$ comparedto the sharp Euclidean estimate.

Pointwise dispersive estimates for Schr\"odinger operators on product cones