  This article studies Volterra evolution equations from the point of view of
control theory, in the case that the generator of the underlying semigroup has
a Riesz basis of eigenvectors. Conditions for admissibility of the system's
control operator are given in terms of the Carleson embedding properties of
certain discrete measures. Moreover, exact and null controllability are
expressed in terms of a new interpolation question for analytic functions,
providing a generalization of results known to hold for the standard Cauchy
problem. The results are illustrated by examples involving heat conduction with
memory.
