We give a sense to certain divergent convolutions of the form $(P \pm i0)^{\lambda} \ast (P \pm i0)^{\mu}$ (see, for the definition of these notations, formulae (2), (4), (5)). As an application of our formulae we obtain the explicit value of a constant which appears in a formula of Fuglede (see [1], p. 7, Lemma 3.1). We observe that many of the "divergences" appearing in quantum field theory are precisely divergent convolutions of the form $(P \pm i0)^{\lambda} \ast (P \pm i0)^{\mu}$ (see [2], pp. 151-183).