Scattering and spectral theory for the linear Boltzmann operator
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.
multiple scattering problem in \(L^ 1\)-space
scientific article; zbMATH DE number 3890181