In mathematics, Schwartz space is the function space of functions all of whose derivatives 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 of S, that is, for tempered distributions. The Schwartz space was named in honour of Laurent Schwartz by Alexander Grothendieck. A function in the Schwartz space is sometimes called a Schwartz function.