An Introduction to Neutrix Composition of Distributions and Delta Function

The composition of the distribution and an infinitely differentiable function having a simple zero at the point is defined by Gel’fand Shilov by the equation It is shown how this definition can be extended to functions which are not necessarily infinitely differentiable or not having simple zeros at the point , by defining as the limit or neutrix limit of the sequence , where is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function A number of examples are given.