Expression of $\int_{\mathbb S^{n-1}}\, e^{-i\left<v,\omega\right>}\,d\sigma(\omega) = ?$

Question

I would like to know what the following integral equals $$\int_{\mathbb S^{n-1}}\, e^{-i\left<v,\omega\right>}\,d\sigma(\omega) = ?,$$ where $S^{n-1}$ is the two-dimentional sphere of $\mathbb R^n$.

Otherwise, if there is a reference, I would be very grateful. Thank you in advance