[see also: account]
In order to make our description of this process precise, we define ...... [Not: “to precise our description”]
We give a fairly simple description of a wide class of averaging operators for which this rate of growth can be seen to be necessary.
Our aim here is to give some sort of `functorial' description of $K$ in terms of $G$.
The description of $Q$ makes it evident that (3) holds. [Note that the it is necessary here.]
What is still lacking is an explicit description of ker$ C$.
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