From semigroups to subelliptic estimates for quadratic operators

Hitrik, Michael; Pravda-Starov, Karel; Viola, Joe

doi:10.1090/tran/7251

From semigroups to subelliptic estimates for quadratic operators
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by Michael Hitrik, Karel Pravda-Starov and Joe Viola PDF

Trans. Amer. Math. Soc. 370 (2018), 7391-7415 Request permission

Abstract:

Using an approach based on the techniques of FBI transforms, we give a new simple proof of the global subelliptic estimates for non-self-adjoint nonelliptic quadratic differential operators, under a natural averaging condition on the Weyl symbols of the operators, established by the second author in Subelliptic estimates for quadratic differential operators (Amer. J. Math. 133 (2011), no. 1, 39–89). The loss of the derivatives in the subelliptic estimates depends directly on algebraic properties of the Hamilton maps of the quadratic symbols. Using the FBI point of view, we also give accurate smoothing estimates of Gelfand–Shilov type for the associated heat semigroup in the limit of small times.

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