Elementary Operations on Distributions

Abstract

In this lesson we intend to extend to distributions several concepts regularly applied to functions such as parity and periodicity, as well as the fundamental notion of derivation. Indeed, it is in the area of differential equations (ordinary and partial) that the use of distributions has been most fruitful. We will illustrate a general method for extending to distributions certain concepts that are known for functions. The difficulty comes from the fact that the argument of a distribution is a function and not a real variable.