An alternate derivation of the Herman-Kluk (coherent state) semiclassical initial value representation of the time evolution operator

It is shown that the Herman-Kluk (or coherent state) initial value representation (IVR) of the semiclassical propagator (time evolution operator) can be obtained by application of a modified Filinov filtering procedure to the standard Van Vleck (coordinate space) expression for the propagator. This further illustrates the effective equivalence, semiclassically, of these various IVRs.