Editing Generalized function (section)

==Schwartz distributions==

The most definitive development was the theory of [[distribution (mathematics)|distributions]] developed by [[Laurent Schwartz]], systematically working out the principle of [[dual space|duality]] for [[topological vector space]]s. Its main rival in [[applied mathematics]] is [[mollifier]] theory, which uses sequences of smooth approximations (the '[[James Lighthill]]' explanation).<ref>Halperin, I., & Schwartz, L. (1952). Introduction to the Theory of Distributions. Toronto: University of Toronto Press. (Short lecture by Halperin on Schwartz's theory)</ref>

This theory was very successful and is still widely used, but suffers from the main drawback that distributions cannot usually be multiplied: unlike most classical [[function space]]s, they do not form an [[algebra]]. For example, it is meaningless to square the [[Dirac delta function]]. Work of Schwartz from around 1954 showed this to be an intrinsic difficulty.