Duality and Distributions: An Application of Topological Vector Spaces

The theory of generalized functions called distributions has a two-fold origin: The problems that created a desire for a generalization of the concept of functions came from classical hard analysis; the methods that provided the solution came from modern structuralist functional analysis. According to the main proponent of the latter, Bourbaki (1960 and 1955), the development of the theory of normed spaces came to a temporary halt after the appearance of Stefan Banach’s book Théorie des opérations linéaires (1932). Instead, functional analysis went in the direction of more general spaces such as locally convex spaces in particular Frechet spaces.