ON THE COMPOSITION AND NEUTRIX COMPOSITION OF THE DELTA FUNCTION AND THE FUNCTION cosh(-1) (vertical bar x vertical bar(1/r) +1)

Fisher B., ÖZÇAĞ E., Al-Sirehy F.

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, vol.13, no.2, pp.161-169, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2017
  • Journal Name: INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.161-169
  • Hacettepe University Affiliated: Yes

Abstract

Let F be a distribution in D' and let f be 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 limit of the sequence {F-n(f(x))}. is equal to h(r), where F-n(x) = F(x) * delta(n)(x) for n = 1, 2, .... and {delta(n)(x)} is a certain regular sequenceconverging to the Dirac delta function. It is proved that the neutrix composition delta(s)[cosh(-1) (x(+)(1/r) +1)] exists and