08-186 Fumio Hiroshima, Sotaro Kuribayashi, Yasumichi Matsuzawa

Strong time operators associated with generalized Hamiltonians (238K, LaTeX 2e) 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 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.

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