Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions

In this paper, we investigate a compactness property of the linearized Boltzmann operator in context polyatomic gas whose molecules undergo resonant collisions. The peculiar structure collision rules allows to tensorize problem into velocity-related one, neighbouring monatomic case, and an internal energy-related one. Our analysis is based on specific treatment energy contributions. We also propose geometric variant Grad's proof same case.