I am looking for a distribution $T:\mathcal D(\mathbb R)\to\mathbb C$ and a test function $\varphi\in C_c^{\infty}(\mathbb R)$ with $$T*\varphi = sin(x),$$ but I can't think of any pair $(T,\varphi)$ that satisfies this convolution. Any idea/ hint would be greatly appreciated.
2026-04-11 16:21:51.1775924511
$T*\varphi=\sin(x)$
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