This article has two objectives. The first is to give a guide to the proof of the (so-called) Casselman-Wallach theorem as it appears in Real Reductive Groups II. The emphasis will be on one aspect of the original proof that leads to the new result i
n this paper which is the second objective. We show how a theorem of van der Noort combined with a clarification of the original argument in my book lead to a theorem with parameters (an alternative is one announced by Berstein and Krotz). This result gives a new proof of the meromorphic continulation of the smooth Eisenstein series.
