  Let the pair of operators, $(H, T)$, satisfy the weak Weyl relation:
$Te^{-itH} = e^{-itH}(T + t)$, where $H$ is self-adjoint and $T$ is closed
symmetric. Suppose that g is a realvalued Lebesgue measurable function on $\RR$
such that $g \in C^2(R K)$ for some closed subset $K \subset \RR$ with Lebesgue
measure zero. Then we can construct a closed symmetric operator $D$ such that
$(g(H), D)$ also obeys the weak Weyl relation.
