Spectral Properties of the Linearized Boltzmann Operator in Lp for 1≤p≤∞

Abstract

The spectrum of both classical and relativistic Boltzmann operator for hard interactions in a whole space is shown to be independent of p in L p for 1≤p < Re λ ≤0. Moreover the resolvent set is independent of p for all 1≤p≤∞ but in L ∞ this operator possesses in addition to the continuous also an uncountable set of point spectrum. © 2013 The Author(s).