Factorial bound for a Volterra iterate
= Factorial bound for a Volterra iterate
{title2=$\|\tau^nf(t)\|\leq\frac{C^nt^n}{n!}\sup_{s\leq t}\|f(s)\|$}
If $\|\tau f(t)\|\leq C\int_0^t\|f(s)\|ds$, repeated integration produces the time-ordered simplex of volume $t^n/n!$. Thus the <Neumann series> $\sum_{n\geq0}\tau^n$ converges on every finite interval, without requiring the single-step <operator norm> to be less than one.