On the Commutative Product of Distributions

Abstract

The commutative products of the distributions x(r) ln(p) vertical bar x vertical bar and x(-r-1) ln(q) vertical bar x vertical bar and of sgn x x(r) ln(P) vertical bar x vertical bar and sgn x x(-r-1) ln(q) vertical bar x vertical bar are evaluated for r = 0, +/- 1, +/- 2,... and p, q = 0, 1, 2,....