= Solution
Use the Fourier convention $\widehat f(\xi)=\int_{\mathbb R^3}e^{-ix\cdot\xi}f(x)\,dx$, with inverse $(2\pi)^{-3}\int e^{ix\cdot\xi}\widehat f(\xi)d\xi$. For a <tempered distribution> $T$, define its <Fourier transform> by duality:
$$
\boxed{\langle\widehat T,\phi\rangle=\langle T,\widehat\phi\rangle,\qquad\phi\in\mathcal S(\mathbb R^3).}
$$
The <Fourier transform> maps the <Schwartz space> continuously onto itself, making the right side a continuous linear functional there. The use of the same negative exponential in the test-function transform is consistent with bilinear distributional pairing; other unitary or sign conventions change the normalization accordingly.
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