Back Espai de Schwartz Catalan Schwartz-Raum German Espacio de Schwartz Spanish Espace de Schwartz French Spazio di Schwartz Italian シュワルツ空間 Japanese 슈바르츠 공간 Korean Przestrzeń Schwartza Polish Пространство Шварца Russian Простір Шварца Ukrainian

Schwartz space

For the Schwartz space of a semisimple Lie group, see Harish-Chandra's Schwartz space. For the Schwartz space of a locally compact abelian group, see Schwartz–Bruhat function.

In mathematics, Schwartz space is the function space of all functions 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 , that is, for tempered distributions. A function in the Schwartz space is sometimes called a Schwartz function.

A two-dimensional Gaussian function is an example of a rapidly decreasing function.

Schwartz space is named after French mathematician Laurent Schwartz.

Developed by StudentB