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$L^1\rightarrow L^\infty$ Dispersive estimates for Coulomb waves. (arXiv:2309.01313v1 [math.AP])

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We show the time decay of spherically symmetric Coulomb waves in $\R^{3}$ for
the case of a repulsive charge. By means of a distorted Fourier transform
adapted to $H=-\Delta+q\cdot |x|^{-1}$, with $q>0$, we explicitly compute the
kernel of the evolution operator $e^{itH}$. A detailed analysis of the kernel
is then used to prove that for large times, $e^{i t H}$ obeys an $L^1 \to
L^\infty$ dispersive estimate with the natural decay rate $t^{-\f32}$.

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