Further results on the neutrix composition of distributions involving the delta function and the function cosh+-1(x1/r+1)$\cosh _ + ^{ - 1}\left( {{x^{1/r}} + 1} \right)$

Abstract

The neutrix composition F(f (x)) of a distribution F(x) and a locally summable function f (x) 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) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function (x). The function cosh+-1(x+1)$\cosh _ + ^{ - 1}\left( {x + 1} \right)$ is defined by

Keywords

• distribution
• dirac-delta function
• composition of distributions
• neutrix
• neutrix limit
• primary 46f10
• secondary 33b10