An introduction to the theory of distributions

Abstract

When working with differential equations, it can be seen that a solution could not always be found. As centuries passed, the notion of the δ "function" started taking shape, as it could help solve these differential equations. Notable mathematicians such as Oliver Heaviside and George Green making contributions towards it. It was not until the early 20th century when P.A.M Dirac used it to further our understanding of Quantum Mechanics. This prompted a need for an entire theory centred around these type of functionals, named "distributions". In this dissertation we will discuss the theory behind distributions as well as arrive to one of its most important theorems, The Ehrenpreis-Malgrange Theorem.