On the Composition of the Distributions X+-R and X+μ

Abstract

Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F n (f)}, where Fn (x) = F (x) * δn (x) and {δn (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function δ (x). The distribution (x+μ)+-r and ( l x lμ)+-r are evaluated for μ > 0, r = 1, 2, ..., and kμ ≠ 1, 2,... © Printed in India.