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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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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Additional Information
  • Michael Hitrik
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California
  • MR Author ID: 657354
  • Email:
  • Karel Pravda-Starov
  • Affiliation: IRMAR, CNRS UMR 6625, Université de Rennes 1, Campus de Beaulieu, 263 avenue du Général Leclerc, CS 74205, 35042 Rennes Cedex, France
  • MR Author ID: 729256
  • Email:
  • Joe Viola
  • Affiliation: Laboratoire de Mathématiques Jean Leray, Université de Nantes, rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
  • Email:
  • Received by editor(s): January 25, 2016
  • Received by editor(s) in revised form: September 5, 2016, and March 28, 2017
  • Published electronically: May 17, 2018
  • Additional Notes: The research of the second and third authors is supported by the ANR NOSEVOL (Project: ANR 2011 BS0101901).
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 7391-7415
  • MSC (2010): Primary 35A22, 35H20, 47D06, 53D22
  • DOI:
  • MathSciNet review: 3841852