Scattering and spectral theory for the linear Boltzmann operator (Q762740)

This paper is concerned with the linear Boltzmann operator (transport operator) in multiple scattering problem in \(L^ 1\)-space. Scattering theory for the linear Boltzmann operator is studied by the Enss method. The author deals only with the inverse wave operator \(\tilde W_+=- \lim_{t\to \infty}e^{tB_ 0}e^{-tB},\) where \(-B_ 0\) and -B are the collisionless Boltzmann operator and the linear Boltzmann operator respectively. He shows that the range of \(\tilde W_+\) is dense in \(L^ 1\). By exploiting this result, he investigates also the spectrum of the operator B. This paper shows that the Enss method is a useful tool in scattering theory even in Banach space, and that scattering theory in Banach space, as well as in Hilbert space, is closely related to spectral theory.