]. A. Alvi, J. Aleman, and . Viola, On weak and strong solution operators for evolution equations coming from quadratic operators, J. Spectr. Theory, vol.8, issue.1, pp.33-121, 2018.

J. M. Bismut, The hypoelliptic Laplacian on the cotangent bundle, J. Amer. Math. Soc, vol.18, issue.2, p.379476, 2005.
DOI : 10.23943/princeton/9780691151298.003.0003

]. J. Bis2 and . Bismut, Hypoelliptic Laplacian and orbital integrals, Annals of Mathematics Studies, vol.177, 2011.

]. A. Lun and . Lunardi, Interpolation Theory, Nuova Serie), 2009.

]. B. Heni, F. Helffer, and . Nier, Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians, Lecture Notes in Mathematics, vol.1862, 2005.

]. B. Heno, J. Helffer, and . Nourrigat, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progress in Mathematics, p.58, 1985.

]. F. Herni, F. Hérau, and . Nier, Isotropic hypoellipticity and trend to equilibrium for the Fokker- Planck equation with a high-degree potential, Arch. Ration. Mech. Anal, vol.171, issue.2, pp.151-218, 2004.

]. M. Hipr and K. Hitrik, Pravda-Starov: Spectra and semigroup smoothing for non-elliptic quadratic operators, Math. Ann, vol.344, issue.4, p.801846, 2009.

. M. Hpv, K. Hitrik, and J. Pravda-starov, Viola: Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators, Bull. Sci. Math, vol.141, issue.7, pp.615-675, 2017.

K. [. Hitrik and J. Pravda-starov, Viola: From semigroups to subelliptic estimates for quadratique operators, Trans. Amer. Math. Soc, 2018.
DOI : 10.1090/tran/7251
URL : http://arxiv.org/pdf/1510.02072

. M. Hsv, J. Hitrik, J. Sjöstrand, and . Viola, Resolvent estimates for elliptic quadratic differential operators, Anal. PDE, vol.6, issue.1, pp.181-196, 2013.

]. L. Hor and . Hörmander, Symplectic classification of quadratic forms, and general Mehler formulas, Math. Z, vol.219, pp.413-449, 1995.

]. Li and . Li, Global hypoellipticity and compactness of resolvent for Fokker-Planck operator, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.11, issue.5 4, pp.789-815, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00422436

]. Li2 and . Li, Compactness criteria for the resolvent of Fokker-Planck operator .prepublication, 1510.

]. J. Sjo and . Sjöstrand, Parametrices for pseudodifferential operators with multiple characteristics, Ark. Mat, vol.12, pp.85-130, 1974.

]. J. Vio and . Viola, Spectral projections and resolvent bounds for partially elliptic quadratic differential operators, J. Pseudo-Diff. Oper. Appl, vol.4, issue.2, pp.145-221, 2013.

J. Viola, The elliptic evolution of non-self-adjoint degree-2 Hamiltonians, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01425703