A RESULT ON DISTRIBUTIONS AND THE CHANGE OF VARIABLE

FISHER B., OZCAG E.

PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.43, sa.3-4, ss.265-272, 1993 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 3-4
  • Basım Tarihi: 1993
  • Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.265-272
  • Hacettepe Üniversitesi Adresli: Evet

Özet

Let F be a distribution in D' and let f be a differentiable function such that f(p+1) is a locally summable function with f'(x) > 0, (or < 0), for all x in the interval (a, b). It is proved that if F is the p-th derivative of a continuous function F(-p) on the interval (f(a), (f(b)), (or (f(b), f(a))), then lim(n-->infinity) integral-infinity/-infinity F(n)(f(x))rho(x)dx = [G, rho] for all rho in D with support contained in the interval (a,b), where F(n)(x) = (F * delta(n))(x). This defines the distribution F(f) = G on the interval (a,b). Some examples are given.