A pseudo-differential calculus on the Heisenberg group

Veronique Fischer, Michael Ruzhansky

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21 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)197-204
JournalComptes Rendus Mathematique
Issue number3
Early online date3 Feb 2014
Publication statusPublished - Mar 2014


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