Commutative convolution of functions and distributions

Fisher B., TAŞ K.

Integral Transforms and Special Functions, vol.18, no.10, pp.689-697, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 10
  • Publication Date: 2007
  • Doi Number: 10.1080/10652460600935965
  • Journal Name: Integral Transforms and Special Functions
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.689-697
  • Keywords: Convolution, Dirac delta function, Distribution
  • Uşak University Affiliated: No

Abstract

The commutative convolution f *g of two distributions f and g in D' is defined as the limit of the sequence {(fτn)* (gτn)}, provided the limit exists, where {τn} is a certain sequence of functions n in D converging to 1. It is proved that equation presented for 0,1,2, , where B denotes the Beta function.