Generalized Function
In mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going to extremes) describing physical phenomena such as point charges. They are applied extensively, especially in physics and engineering.
A common feature of some of the approaches is that they build on operator aspects of everyday, numerical functions. The early history is connected with some ideas on operational calculus, and more contemporary developments in certain directions are closely related to ideas of Mikio Sato, on what he calls algebraic analysis. Important influences on the subject have been the technical requirements of theories of partial differential equations, and group representation theory.
Read more about Generalized Function: Some Early History, Schwartz Distributions, Algebras of Generalized Functions, Other Theories, Topological Groups, Generalized Section
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