  The operator of double differentiation on a finite interval with Robin
boundary conditions perturbed by the composition of a Volterra convolution
operator and the differentiation one is considered. We study the inverse
problem of recovering the convolution kernel along with a coefficient of the
boundary conditions from the spectrum. We prove the uniqueness theorem and that
the standard asymptotics is a necessary and sufficient condition for an
arbitrary sequence of complex numbers to be the spectrum of such an operator. A
constructive procedure for solving the inverse problem is given.
