International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 60129, 9 pages
doi:10.1155/2007/60129
Research Article

On the Composition of Distributions x−sln|x| and |x|μ

Biljana Jolevska-Tuneska1 and Emin Özçāg2

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

Received 31 January 2007; Revised 11 May 2007; Accepted 12 June 2007

Academic Editor: Michael M. Tom

Copyright © 2007 Biljana Jolevska-Tuneska and Emin Özçāg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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,….