Further Results on Colombeau Product of Distributions

In quantum physics one finds the need to evaluate δ, when calculating the transition rates of certain particle interactions; see [1]. The problem of defining products of distributions is also closely connected with the problem of renormalization in quantum field theory. Due to the large use of distributions in the natural sciences and other mathematical fields, the problem of the product of distributions [2] is an objective of many research studies. Starting with the historically first construction of distributional multiplication by König [3], and the sequential approach developed in [4] by Antosik et al., there have been numerous attempts to define products of distributions, see [5–7], or rather to enlarge the number of existing products. Having a look at the theory of distributions [8, 9] we realize that there are two complementary points of view.