On the composition of the distributions x+-r and x+μ

Fisher B., TAŞ K.

Indian Journal of Pure and Applied Mathematics, vol.36, no.1, pp.11-22, 2005 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2005
  • Journal Name: Indian Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.11-22
  • Keywords: Composition of distributions, Delta function, Distribution, Neutrix, Neutrix limit
  • Uşak University Affiliated: No

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.