Bounds for the state-modulated resolvent of a linear Boltzmann generator (Q2895727)

The authors study the generator \(L\) of a special Markov semigroup. This generator appears in a linear Boltzmann equation modeling a one-dimensional test particle in a periodic potential colliding with particles from ideal background gas. An estimate for the generalized resolvent \((L-M_h)^{-1}\) is obtained. Here \(M_h\) is an operator of multiplication by a bounded measurable function \(h\). The estimate is related to the typical amount of time spent by a particle in various regions of phase space before arriving at a region around the origin.