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When Schroedinger propagator commutes other operators?

Let $f\in \mathcal{S}(\mathbb R^d)$ (Schwartz Space). We know that $\widehat{\nabla f}(\xi)= 2 \pi i \xi \hat{f} (\xi). $ We define $$\widehat{|\nabla| f^{s}} (\xi) = (2 \pi |\xi|)^s \hat{f} (\xi), …
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