  We highlight Hermiticity issues in bound-state equations whose kernels are
subject to a highly asymmetric mass and momentum distribution and whose
eigenvalue spectrum becomes complex for radially excited states. We trace back
the presence of imaginary components in the eigenvalues and wave functions to
truncation artifacts and suggest how they can be eliminated in the case of
charmed mesons. The solutions of the gap equation in the complex plane, which
play a crucial role in the analytic structure of the Bethe-Salpeter kernel, are
discussed for several interaction models and qualitatively and quantitatively
compared to analytic continuations by means of complex-conjugate pole models
fitted to real solutions.
