An extension of the distributional composition of (sgn x|x|α) and x−r for negative integers
Functiones et Approximatio, Commentarii Mathematici, ss.1-14, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.7169/facm/260209-16-3
- Dergi Adı: Functiones et Approximatio, Commentarii Mathematici
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
- Sayfa Sayıları: ss.1-14
- Anahtar Kelimeler: composition, distribution, neutrix, neutrix limit, regular sequence, singular distribution
- Hacettepe Üniversitesi Adresli: Evet
Özet
In the theory of Schwartz distributions there is no reasonable ways of introducing the form F (f (x)) where F and f are distributions. However, the composition F (f) of a distribution F and a locally summable function f is defined as the neutrix limit of the regular sequence {Fn(f)}, where Fn(x) = F (x) * δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function δ(x). The composition of the locally summable function (sgn x|x| α) and the singular distribution x-r were defined by Fisher and Tuneska in [6] for r = 1, 2,. .., α > 0 and rα /∈ Z-. In this paper we extend their definition for r = 1, 2,. .., α > 0 and rα ∈ Z-.