Abstract
Let the pair of operators, (H, T), satisfy the weak Weyl relation:
where H is self-adjoint and T is closed symmetric. Suppose that g is a real-valued Lebesgue measurable function on \({\mathbb {R}}\) such that \({g\in C^2(\mathbb {R}\backslash K)}\) for some closed subset \({K\subset\mathbb {R}}\) with Lebesgue measure zero. Then we can construct a closed symmetric operator D such that (g(H), D) also obeys the weak Weyl relation.
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Hiroshima, F., Kuribayashi, S. & Matsuzawa, Y. Strong Time Operators Associated with Generalized Hamiltonians. Lett Math Phys 87, 115–123 (2009). https://doi.org/10.1007/s11005-008-0287-y
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DOI: https://doi.org/10.1007/s11005-008-0287-y