An Easy Approach to Distributions and Operational Calculus

Abstract

The Mikusinski space is introduced as the smallest extension of the space of classical continuous functions in which the integration operator is bijective. (This can be viewed as a very small part of the field of Mikusinski operators.) It is shown that the space of Schwartz distributions (of finite order) can be defined as a quotient of the Mikusinski space. A remarkable property of Mikusinski functions is that they admit multiplication by all rational functions. It is demonstrated that this multiplication provides a natural simple basis for Heaviside's operational calculus.