From semigroups to subelliptic estimates for quadratic operators
Analysis of PDEs
2016-09-27 v2 Spectral Theory
Abstract
Using an approach based on the techniques of FBI transforms, we give a new simple proof of the global subelliptic estimates for non-selfadjoint non-elliptic quadratic differential operators, under a natural averaging condition on the Weyl symbols of the operators, established by the second author. 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.
Cite
@article{arxiv.1510.02072,
title = {From semigroups to subelliptic estimates for quadratic operators},
author = {Michael Hitrik and Karel Pravda-Starov and Joe Viola},
journal= {arXiv preprint arXiv:1510.02072},
year = {2016}
}