FURTHER RESULTS ON THE NEUTRIX COMPOSITION OF THE DELTA FUNCTION

Abstract

Let F be a distribution inD and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x)=F(x)∗ δn(x) forn =1 ,2,... and {δn(x)} is a certain regular sequence converging to the Dirac delta. It is proved that the neutrix composition δ(s)[lnr(1 + x1/r + )] exists and is given