An extension of the definition on the compositions of the singular distributions

ÖZÇAĞ E.

Turkish Journal of Mathematics, vol.48, no.2, pp.279-295, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3506
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.279-295
  • Keywords: Dirac-delta function, distribution, divergent integral, Hadamard’s finite part, neutrices, Regular sequence
  • Hacettepe University Affiliated: Yes

Abstract

Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g−) for a locally summable function g(x).