Boltzmann Volterra operator ($(\tau f)(t)={\int }_0^t{U}_a(t,s)K_{s}f(s)ds$)

Combine the damped free-transport evolution and the linear Boltzmann collision operator in a time-ordered Bochner integral. Its norm obeys $\Vert \tau f(t){\Vert }_2\le C{\int }_0^t\Vert f(s){\Vert }_{2}ds$. This reduces the characteristic integral equation to $(I-\tau )f=U_a(t,0)f_0$.