Fumio Hiroshima, Sotaro Kuribayashi, Yasumichi Matsuzawa
Strong time operators associated with generalized Hamiltonians
(238K, LaTeX 2e)

ABSTRACT.   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 $g in C^2(\mathbb{R} \setminus K)$ for some $K \subset 
\mathbb{R}$ with Lebesgue measure zero and that $lim_{|\lambda| \to \infty} 
g(\lambda)e^{-\beta\lambda^2} = 0$ for all $\beta > 0$. Then we can construct a 
closed symmetric operator $D$ such that #(g(H), D)$ also obeys the weak Weyl 
relation.