Editing Generalized function (section)

{{Short description|Objects extending the notion of functions}}
In [[mathematics]], '''generalized functions''' are objects extending the notion of [[function (mathematics)|function]]s on real or complex numbers. There is more than one recognized theory, for example  the theory of [[distribution (mathematics)|distributions]]. Generalized functions are especially useful for treating [[discontinuous function]]s more like [[smooth function]]s, and describing discrete physical phenomena such as [[point charge]]s. They are applied extensively, especially in [[physics]] and [[engineering]]. Important motivations have been the technical requirements of theories of [[partial differential equation]]s and [[group representation|group representations]].

A common feature of some of the approaches is that they build on [[Operator (mathematics)|operator]] aspects of everyday, numerical functions. The early history is connected with some ideas on [[operational calculus]], and some contemporary developments are closely related to [[Mikio Sato]]'s [[algebraic analysis]].