Note that although the point \(k = k_* = \sqrt{\omega ^2 -1}\) (as well as the symmetric ones) is not a pole but a quasi-singularityquasi-singularity. Namely, the inverse Fourier transform integral over a small (but nonzero) segment, \(- \varepsilon < k- k_* < \varepsilon ,\, \varepsilon > 0\), leads to an asymptotic representation of the wave.