  Quasinormal modes and grey-body factors are spectral characteristics
corresponding to different boundary conditions: the former imply purely
outgoing waves to the event horizon and infinity, while the latter allow for an
incoming wave from the horizon, thus describing a scattering problem.
Nevertheless, we show that there a link between these two characteristics. We
establish an approximate correspondence between the quasinormal modes and
grey-body factors, which becomes exact in the high-frequency (eikonal) regime.
We show that, in the eikonal regime, the grey-body factors of spherically
symmetric black holes can be remarkably simply expressed via the fundamental
quasinormal mode, while at smaller l, the correction terms include values of
the overtones. This might be interesting in the context of the recently
observed connection between grey-body factors and the amplitudes of
gravitational waves from black holes. The correspondence might explain why
grey-body factors are more stable, i.e. less sensitive, than higher overtones
to small deformation of the effective potential.
