On the multiplicative products of the n-dimensional distributional Hankel transforms

摘要

In this note, we prove several multiplicative products of the n-dimensional Hankel transform. In fact the following formulae:H{δ(k)(u(x))}·H{δ(ℓ)(u(x))}=DHδk+ℓ+n−22(u(x)),H{δ(k)(P)}·H{δ(ℓ)(P)}=CHδk+ℓ+n−22(P),H{δ(k)(|x|2)}·H{δ(ℓ)(|x|2)}=CHδk+ℓ+n−22(|x|2),We observe that the above results were inspirated in a non-edited paper due to Manuel Aguirre Téllez [cf. The Hankel transform of the kth derivative of Dirac delta in u(x1,x2,…,xn), in press].