International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 60129, 9 pages
doi:10.1155/2007/60129
On the Composition of Distributions x−sln|x| and |x|μ
Biljana Jolevska-Tuneska1
and Emin Özçaḡ2
1Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University - Skopje, Karpos II bb, Skopje 1000, Macedonia
2Department of Mathematics,, Faculty of Science, University of Hacettepe, Beytepe 06532, Ankara, Turkey
Abstract
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 {Fn(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 composition of the distributions x−sIn|x| and |x|μ is evaluated for s=1,2,…,μ>0 and μs≠1,2,….