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

ÖZÇAĞ E.

Turkish Journal of Mathematics, cilt.48, sa.2, ss.279-295, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.55730/1300-0098.3506
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.279-295
  • Anahtar Kelimeler: Dirac-delta function, distribution, divergent integral, Hadamard’s finite part, neutrices, Regular sequence
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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).