Volterra series for the linear Boltzmann equation
= Volterra series for the linear Boltzmann equation
{c}
{title2=$f=\sum_{n\geq0}\tau^nF$}
The <factorial bound for a Volterra iterate> gives convergence in the space of bounded strongly measurable $L^2$-valued functions on $[0,T]$. The sum solves $(I-\tau)f=F$, where $F=U_a(t,0)f_0$, and satisfies $\sup_{t\leq T}\|f(t)\|_2\leq e^{CT}\|f_0\|_2$. Applying the same iterate bound to a difference $g=\tau g$ proves uniqueness on every finite interval.