Exponential convergence for the linear homogeneous Boltzmann equation for hard potentials

In this paper, we consider the asymptotic behavior of solutions to the linear spatially homogeneous Boltzmann equation for hard potentials without angular cutoff. We obtain an optimal rate of exponential convergence towards equilibrium in a L1-space with a polynomial weight. Our strategy is taking advantage of a spectral gap estimate in the Hilbert space L2(μ−12) and a quantitative spectral mapping theorem developed by Gualdani et al. (2017).