  Controllability of the heat equations with memory (of Gurtin-Pipkin type) has
been studied using several methods with the following in common: the existing
results on controllability of the (memoryless) wave equation are lifted to the
equation with memory.
  Here we revisit the approach based on operator methods (cosine operators) and
we improve the results obtained in a previous paper (L. Pandolfi: "The
controllability of the Gurtin-Pipkin equation: a cosine operator approach:,
Appl.Math. and Optim. 52, 143-165, 2005. In particular we identify the control
time.
