On the composition of the distributions x-1 ln| x | and x r+

Fisher B., TAŞ K.

Integral Transforms and Special Functions, cilt.16, sa.7, ss.533-543, 2005 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 7
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1080/10652460500105438
  • Dergi Adı: Integral Transforms and Special Functions
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.533-543
  • Anahtar Kelimeler: Composition of distributions, Delta-function, Distribution, Neutrix, Neutrix limit
  • Uşak Üniversitesi Adresli: Hayır

Özet

Let F be a distribution and let f be a locally summable function. The distribution F( f )is defined as the neutrix limit of the sequence { F n( 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 distribution (xr+)-1is ln |xr +|is evaluated for r = 1, 2, ....