In this note, convolutional systems in the behavioral approach are considered. Convolutional equations generalize both differential and delay-differential systems. Three fundamental problems are treated and solved in this note. The first consists in characterizing when two kernel representations are equivalent, which means to determine when two different convolutional equations provide the same set of solutions. The second problem considered in this note concerns the characterization of the spectral controllability for this class of systems. Finally, this note provides a partial solution of the so called latent variable elimination problem, which is one of the basic steps of the modeling procedure in the behavioral approach.