  In this work, a general definition of convolution between two arbitrary
Tempered Ultradistributions is given. When one of the Tempered
Ultradistributions is rapidly decreasing this definition coincides with the
definition of J. Sebastiao e Silva. In the four-dimensional case, when the
Tempered Ultradistributions are even in the variables $k^0$ and $\rho$ (see
Section 5) we obtain an expression for the convolution, which is more suitable
for practical applications. The product of two arbitrary even (in the variables
$x^0$ and $r$) four dimensional distributions of exponential type is defined
via the convolution of its corresponding Fourier Transforms. With this
definition of convolution, we treat the problem of singular products of Green
Functions in Quantum Field Theory. (For Renormalizable as well as for
Nonrenormalizable Theories). Several examples of convolution of two Tempered
Ultradistributions are given. In particular we calculate the convolution of two
massless Wheeeler's propagators and the convolution of two complex mass
Wheeler's propagators.
