Schwartz function

In mathematics, Schwartz space ${\displaystyle {\mathcal {S}}}$ is the function space of all functions whose derivatives of all orders are rapidly decreasing. This space has the important property that the Fourier transform is an automorphism on this space. This property enables one, by duality, to define the Fourier transform for elements in the dual space ${\displaystyle {\mathcal {S}}^{*}}$ of ⁠${\displaystyle {\mathcal {S}}}$⁠, that is, for tempered distributions. A function in the Schwartz space is sometimes called a Schwartz function.