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 xsIn|x| and |x|μ is evaluated for s=1,2,,μ>0 and μs1,2,.