ON THE COMPOSITION OF THE DISTRIBUTIONS x(-1) ln(m) vertical bar x vertical bar AND x(r)

Fisher B., Ege I., ÖZÇAĞ E.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.37, no.1, pp.1-8, 2008 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 1
  • Publication Date: 2008
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1-8
  • Hacettepe University Affiliated: Yes

Abstract

Let F be a distribution and f a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function delta(x). The composition of the distributions x(-1) ln(m) vertical bar x vertical bar and x(r) is evaluated for r, m = 1, 2, 3....