  The Molchanov's condition is a necessary condition for the compactness of the
resolvent for a wide class of ordinary differential operators of arbitrary
order, but for the Sturm-Liouville operator it is not sufficient, even if the
real part of the potential is non-negative. Molchanov's criterion remains valid
in the formulation closest to the original one for potentials that take values
in a narrower sector than the half-plane, separated from the negative
half-axis. This work is devoted to these questions.
