Schwartz space
Function space of all functions whose derivatives are rapidly decreasing / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Schwartz function?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
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.
Schwartz space is named after French mathematician Laurent Schwartz.