A commutative neutrix product of ultradistributions

Fisher B., Kiliçman A.

Integral Transforms and Special Functions, vol.4, no.1-2, pp.77-82, 1996 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1-2
  • Publication Date: 1996
  • Doi Number: 10.1080/10652469608819095
  • Journal Name: Integral Transforms and Special Functions
  • Journal Indexes: Scopus
  • Page Numbers: pp.77-82
  • Keywords: Delta- function, Distribution, Fourier transform, Neutrix, Neutrix limit, Neutrix product, Ultradistribution
  • Ondokuz Mayıs University Affiliated: Yes


Let f and g be distributions in script D sign′ and let fn(x) = f(x)κn(x), gn(x) = g(x)κn(x), where κn(x) is a certain function which converges to the identity function as n tends to infinity. Then the commutative neutrix convolution product f △ g is defined as the neutrix limit of the sequence {fn * gn}, provided the limit h exists in the sense that N-limn→∞〈fn * gn, ∅〉 = 〈h, ∅〉 for all ∅ ∈ script D sign. If now δn(σ) = (2π)±1ℱ(κn), where ℱ denotes the Fourier transform, then the neutrix product f̄△ḡ is defined by equation f̄△ḡ = ℱ(f △ g). Some results are given.