Convolution of ultradistributions and field theory

A general definition of convolution between two arbitrary tempered ultradis tributions is given. When one of the tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. The product of two arbitrary distributions of exponential type is d efined via the convolution of its corresponding Fourier transforms. Several examples of convolution of two tempered ultradistributions and singular pr oducts are, given. In particular, we reproduce the results obtained by A. G onzales Dominguez nd A. Bredimas.