Let the pair of operators, (H, T), satisfy the weak Weyl relation: Te -itH =e-itH where H is self-adjoint and T is closed symmetric. Suppose that g is a real-valued Lebesgue measurable function on ℝ such that g ∈ c2(ℝ\K) for some closed subset K ⊂ ℝ with Lebesgue measure zero. Then we can construct a closed symmetric operator D such that (g(H), D) also obeys the weak Weyl relation.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics