  We consider the problem of uniqueness of the kernel in the nonlocal theory of
accelerated observers. In a recent work, we showed that the convolution kernel
is ruled out as it can lead to divergences for nonuniform accelerated motion.
Here we determine the general form of bounded continuous kernels and use
observational data regarding spin-rotation coupling to argue that the kinetic
kernel given by $K(\tau ,\tau')=k(\tau')$ is the only physically acceptable
solution.
