Fourier transform of a compactly supported distribution
= Fourier transform of a compactly supported distribution
For $u\in\mathcal E'(\mathbb R^n)$, its <Fourier transform> is the <smooth function>
$$
\widehat u(\lambda)=\langle u(x),e^{-i\lambda\cdot x}\rangle.
$$
It has at most <polynomial growth>, and its extension to complex frequency is controlled more precisely by the <Paley–Wiener–Schwartz theorem>.