2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71552We 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.Spectral TheoryMathematical Physics35P20; 35S10; 47A10; 47D06text