On the non-commutative neutrix product of the distributions and

Abstract

Let f and g be distributions and g n = (g*δ n )(x), where δ n (x) is a certain sequence converging to the Dirac delta-function. The non-commutative neutrix product f ° g of f and g is defined to be the neutrix limit of the sequence {fg n }, provided its limit h exists in the sense that for all functions ϕ in 𝒟. It is proved that for μ < r−1; μ≠0,±1,±2, …, r = 1, 2, … and p, q = 0, 1, 2….