  We perform a reanalysis of the energy levels obtained in a recent lattice QCD
simulation, from where the existence of bound states of $KD$ and $KD^*$ are
induced and identified with the narrow $D_{s0}^*(2317)$ and $D_{s1}^*(2460)$
resonances. The reanalysis is done in terms of an auxiliary potential,
employing a single-channel basis $KD^{(*)}$, and a two-channel basis $KD^{(*)},
\eta D_s^{(*)}$. By means of an extended L\"uscher method we determine poles of
the continuum $t$-matrix, bound by about 40 MeV with respect to the $KD$ and
$KD^*$ thresholds, which we identify with the $D_{s0}^*(2317)$ and
$D_{s1}^*(2460)$ resonances. Using a sum rule that reformulates Weinberg
compositeness condition we can determine that the state $D_{s0}^*(2317)$
contains a $KD$ component in an amount of about 70%, while the state
$D_{s1}^*(2460)$ contains a similar amount of $KD^*$. We argue that the present
lattice simulation results do not still allow us to determine which are the
missing channels in the bound state wave functions and we discuss the necessary
information that can lead to answer this question.
