This is my first post here, so bear with me ;)


In wikipedia and other references, [**Schwartz space**](http://en.wikipedia.org/wiki/Schwartz_space) is defined as the set of inﬁnitely differentiable functions on $\mathbb{R}^n$. On the other hand, A locally convex space X is named a **LS-space** if there is a Fréchet-Schwartz space Y such that the strong dual $Y^{'}$ is isomorphic to X. (Naturally, A **Fréchet-Schwartz** space is a Fréchet space which is at the same time a Schwartz space). It seems to me that Schwartz spaces in the definition of Fréchet-Schwartz spaces and LS-spaces are considerably different than the definition given in wikipedia. After all they have to be defined in the context of locally convex spaces. I appreciate it if someone could clarify the definition of Schwartz space here.



Schwartz space defined on locally convex spaces
*The* Schwartz space (of infinitely differentiable functions) is just an example of *a* Schwartz space. The term “Schwartz space” is used for two concepts. The German Wikipedia has two articles: [Schwartz-Raum](http://de.wikipedia.org/wiki/Schwartz-Raum) and [Schwartz-Raum (allgemein)](http://de.wikipedia.org/wiki/Schwartz-Raum_%28allgemein%29), which includes a [bibliography](http://de.wikipedia.org/wiki/Schwartz-Raum_%28allgemein%29#Literatur).


