Journal of Mathematical Analysis and Applications, vol.306, no.1, pp.364-374, 2005 (SCI-Expanded)
The non-commutative convolution f * g of two distributions f and g in D′ is defined to be the limit of the sequence {(fτn) * g}, provided the limit exists, where {τn} is a certain sequence of functions in D converging to 1. It is proved that x λ * (sgnx x μ) = 2 sin(λπ/2)cos(μπ/2)/sin[(λ + μ)π/2] B(λ + 1, μ + 1) sgn x x λ+μ+1, for - 1 < λ + μ < 0 and λ, μ≠ - 1, - 2,..., where B denotes the Beta function. © 2005 Elsevier Inc. All rights reserved.