Exercise 2.18 (Wave propagators). Using the spatial Fourier transform, show that if $u\in C_{t,\mathrm{loc}}^2\mathcal{S}_x(\mathbb{R}\times\mathbb{R}^d)$ is a field obeying the wave equation (2.9) with $c=1$, then $$\widehat{u(t)}(\xi)=\cos(t\lvert\xi\rvert)\widehat{u}_0(\xi)+\frac{\sin(t\lvert\xi\rvert)}{\lvert\xi\rvert}\widehat{u}_1(\xi)$$ for all $t\in\mathbb{R}$ and $\xi\in\mathbb{R}^d$; one can also write this as $$u(t)=\cos(t\sqrt{-\Delta})u_0+\frac{\sin(t\sqrt{-\Delta})}{\sqrt{-\Delta}}u_1$$
What exactly does $\sqrt{-\Delta}$ mean in Fourier transform in this text?