  In this work we shall prove new results on the theory of convolution
operators on spaces of entire functions. The focus is on hypercyclicity results
for convolution operators on spaces of entire functions of a given type and
order; and existence and approximation results for convolution equations on
spaces of entire functions of a given type and order. In both cases we give a
general method to prove new results that recover, as particular cases, several
results of the literature. Applications of these more general results are
given, including new hypercyclicity results for convolution operators on spaces
on entire functions on $\mathbb{C}^n.$
