RESULTS ON THE NEUTRIX COMPOSITION OF THE DELTA FUNCTION

Fisher B., Kraiweeradechachai T., ÖZÇAĞ E.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.36, sa.2, ss.147-156, 2007 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 2
  • Basım Tarihi: 2007
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.147-156
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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