  The problem of renormalization in perturbative quantum field theory (pQFT)
can be described in a rigorous way through the theory of extension of
distributions. In the framework of pQFT a certain type of distribution appears,
given by products of Green functions which act by integration with a test
function. They present ultraviolet divergences, whenever any pair of arguments
coincide on one point of spacetime, and therefore, they are not defined
everywhere. In this work we have studied the necessary and sufficient
conditions for the extension (or regularization) of this type of distribution.
Moreover, we have constructed such extensions explicitly, satisfying a series
of physically relevant axioms, such as the axiom of causality.
