Distribution Theory

Recall in Sect. 1.10, the Dirac delta were introduced in (1.10.6) with no mathematical foundations, and we mentioned that a rigorous analysis was needed to validate the construction of delta. This is one of the main motivations to develop the theory of distribution, and the purpose of this chapter is to introduce the theory to the reader and discuss its most important basics. As explained earlier, the Dirac delta cannot be considered as a function. We shall call these mathematical objects: distributions. Distributions are not functions in the classical sense because they exhibit some features that are beyond the definition of the function.