  The inverse spectral problem is studied for the Sturm-Liouville operator with
a complex-valued potential and arbitrary entire functions in one of the
boundary conditions. We obtain necessary and sufficient conditions for
uniqueness, and develop a constructive algorithm for the inverse problem
solution. The main results are applied to the Hochstadt-Lieberman half-inverse
problem. As an auxiliary proposition, we prove local solvability and stability
for the inverse Sturm-Liouville problem by the Cauchy data in the
non-self-adjoint case.
