Semiclassical analysis for the Kramers-Fokker-Planck equation
  We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and precise resolvent estimates inside the pseudo-spectrum. We apply our results to the Kramers-Fokker-Planck operator. 
Frederic Herau, Johannes Sjoestrand, Christiaan C. Stolk