A Commutative Neutrix Product of Ultradistributions

Abstract

Let f and g be distributions in D' and let f(n)(x) = f(x)kappa(n)(x), g(n)(x) = g(x)kappa(n)(x), where kappa(n)(x) is a certain function which converges to the identity function as n tends to infinity. Then the commutative neutrix convolution product f (sic) g is defined as the neutrix limit of the sequence {f(n) * g(n)}, provided the limit h exists in the sense that [GRAPHICS] for all phi is an element of D. If now delta(n)(sigma) = (2 pi)(-1) F(kappa(n)), where F denotes the Fourier transform, then the neutrix product (f) over tilde Delta (h) over tilde is defined by equation (f) over tilde Delta (g) over tilde = F (f (sic) g). Some results are given.