Funktsionaal
Funktsionaal, or functional in English, is a map that assigns a single scalar value to a function. In mathematics, functionals typically act on spaces of functions and take values in the real or complex numbers. They are studied within functional analysis and appear in many areas, including calculus of variations, partial differential equations, and optimization. Functionals are defined on spaces such as C[a,b], L^p[a,b], or Sobolev spaces, and their properties depend on the topological structure of the domain.
A central distinction is between linear and nonlinear functionals. A functional F is linear if F(αf +
Representation and duality are key themes. In a Hilbert space H, every continuous linear functional F appears