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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 ?

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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 $D(\Omega)$.

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  • $\begingroup$ I wondered about that, but then it's $D$ $'$ that has the distributions rather than $D$ ? $D$ has the test functions. $\endgroup$ – Tom Collinge Nov 8 '16 at 6:54

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