Journal
COMPTES RENDUS MATHEMATIQUE
Volume 352, Issue 3, Pages 197-204Publisher
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
DOI: 10.1016/j.crma.2013.12.006
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Funding
- London Mathematical Society
- University of Padua
- EPSRC Leadership Fellowship [EP/G007233/1]
- EPSRC [EP/K039407/1]
- EPSRC [EP/K039407/1, EP/G007233/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/G007233/1, EP/K039407/1] Funding Source: researchfish
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In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,2,3] of pseudo-differential calculi on graded groups. The relation between the Weyl quantisation and the representations of the Heisenberg group enables us to consider here scalar-valued symbols. We find that the conditions defining the symbol classes are similar but different to the ones in [1]. Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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