ON THE COMPOSITION OF THE DISTRIBUTIONS xλ+ lnm x+ AND xμ+

Abstract

Let F be a distribution and let f be a locally summable function.

The neutrix composition F (f ), of F and 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 neutrix composition of the distributions λmμ

x+ln x+ andx+ isevaluatedfor−1<λ<0, μ>0,λμ̸=−1,−2,... and m = 0,1,2,....