 08186 Fumio Hiroshima, Sotaro Kuribayashi, Yasumichi Matsuzawa
 Strong time operators associated with generalized Hamiltonians
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Oct 13, 08

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Abstract. Let the pair of operators, $(H, T)$, satisfy the weak Weyl relation:
$Te^{itH} = e^{itH} (T + t)$, where $H$ is selfadjoint 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.
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