RESULTS ON THE NEUTRIX COMPOSITION OF THE DELTA FUNCTION


Fisher B., Kraiweeradechachai T., ÖZÇAĞ E.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.36, no.2, pp.147-156, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 2
  • Publication Date: 2007
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.147-156
  • Hacettepe University Affiliated: Yes

Abstract

Let F be a distribution in D' and f a locally summable function. The composition F(f (x)) of F and f is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {F-n(f(x))} is equal to h(x), where F-n(x) = F(x) * delta(n)(x) for n = 1, 2.... and {delta(n)(x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition delta((s))[ln(r)(1 + vertical bar x vertical bar)] exists and that