Suppose \(f\in \mathcal{S}(R^n)\). Then the Fourier transform \(\mathcal{F}f\) is smooth, with
\[ \partial^{\alpha} \mathcal{F}f = (-i)^{\lvert \alpha\rvert}\mathcal{F}(x^{\alpha}f). \]Suppose \(f\in \mathcal{S}(R^n)\). Then the Fourier transform \(\mathcal{F}f\) is smooth, with
\[ \partial^{\alpha} \mathcal{F}f = (-i)^{\lvert \alpha\rvert}\mathcal{F}(x^{\alpha}f). \]