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∈C2(RK) 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.Comment: 10 page