Page "Functional analysis" Paragraph 1

The usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function and the name was first used in Hadamard's 1910 book on that subject.

However, the general concept of functional had previously been introduced in 1887 by the Italian mathematician and physicist Vito Volterra.

The theory of nonlinear functionals was continued by students of Hadamard, in particular Fréchet and Lévy.

Hadamard also founded the modern school of linear functional analysis further developed by Riesz and the group of Polish mathematicians around Stefan Banach.