# Why “D” for the space of smooth functions with compact support?

The Schwartz space of smooth rapidly vanishing functions seems to generally be notated as "S" which I guess is for Schwartz.

It has a subspace consisting of smooth functions with compact support which seems to generally be notated as "D" - does anyone know why ?

I am not sure, but I would guess that "D" is for "distribution". For $\Omega \subset \Bbb R^d$, a distribution on $\Omega$ is a continuous (with respect to the limit inductive topology) linear form on $D(\Omega)$.
• I wondered about that, but then it's $D$ $'$ that has the distributions rather than $D$ ? $D$ has the test functions. – Tom Collinge Nov 8 '16 at 6:54