Defining Compositions of x(mu)+, |x|(mu), x(-s), and x(-s) ln |x| as Neutrix Limit of Regular Sequences


ÖZÇAĞ E., Lazarova L., Jolevska-Tuneska B.

COMMUNICATIONS IN MATHEMATICS AND STATISTICS, vol.4, no.1, pp.63-80, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1007/s40304-015-0076-8
  • Journal Name: COMMUNICATIONS IN MATHEMATICS AND STATISTICS
  • Journal Indexes: Emerging Sources Citation Index, Scopus
  • Page Numbers: pp.63-80

Abstract

In this paper the compositions (x(+)(mu))(-s)(-)(x(+)(mu))(-s)(+), (|x| mu)(-s) (-) and (| x|(mu))(-s)(+) of distributions x(+)(mu), |x|(mu) and x(-s) are considered. They are defined via neutrix calculus for mu > 0, s = 1, 2,... and mu s epsilon Z(+). In addition, the composition of x(-s) ln|x| and x(+)(r) is also defined for r, s epsilon Z(+).