Volterra convolution of kernels ($(A\ast B)(t)={\int }_0^{t}A(t-s)B(s)ds$)

For time-dependent integral kernels on a Riemannian manifold, composition also integrates over the intermediate point: $(A\ast B)(t,x,y)={\int }_0^t{\int }_{M}A(t-s,x,z)B(s,z,y)d{V}_{z}ds$. It is associative under the usual absolute-integrability hypotheses. The integration simplex gives factorial bounds for iterated convolutions of bounded kernels.