= Integrable Volterra solution for normalized velocity relaxation
{title2=$f=\sum_{j\geq0}\tau^jU_\cdot f_0$}
For $E=L^1_{x,v}$, let $(\tau f)(t)=\int_0^tU_{t-s}(P-I)f(s)ds$. The <factorial bound for a Volterra iterate> is $\|\tau^nf(t)\|_1\leq(2t)^n\sup_{s\leq t}\|f(s)\|_1/n!$. Thus the <Neumann series> converges in $C([0,T];E)$ for every finite $T$ and solves $f=U_\cdot f_0+\tau f$. The same estimate applied to a difference proves uniqueness among locally time-bounded <integral> solutions. The whole collision term remains inside this undamped <integral>, rather than absorbing loss into the free propagator.
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