\[\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\mathcal{H}\mskip-3.0muf\mskip 3.0%
mu\left(u\right){\mathrm{e}}^{\mathrm{i}ux}\,\mathrm{d}u=-\mathrm{i}(%
\operatorname{sign}x)\mathscr{F}\mskip-3.0muf\mskip 3.0mu\left(x\right),\]