The product of convolution Pλ± ∗ Pμ∓ and the multiplicative product Pλ± · δκ(P±)

In this note, we give a sense to the products of convolution Pλ+ ∗ Pμ+· Pλ−∗Pμ− and eλπiPλ+∗Pμ−+eλπiPλ−∗Pμ+), where λ and μ are complex numbers and pλ± are defined by the formulas (1.2) and (1.10). A very interesting conclusion appears in Section 3 (cf. (3.1) and (3.2)).