Generalized function

Objects extending the notion of functions

In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful for treating discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering. Important motivations have been the technical requirements of theories of partial differential equations and group representations.

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