A pseudo-differential calculus on the Heisenberg group

Veronique Fischer, Michael Ruzhansky

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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
Volume352
Issue number3
Early online date3 Feb 2014
DOIs
Publication statusPublished - Mar 2014

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Differential Calculus
Heisenberg Group
Hypoellipticity
Quantization
Scalar
Estimate

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A pseudo-differential calculus on the Heisenberg group. / Fischer, Veronique; Ruzhansky, Michael.

In: Comptes Rendus Mathematique, Vol. 352, No. 3, 03.2014, p. 197-204.

Research output: Contribution to journalArticle

Fischer, Veronique ; Ruzhansky, Michael. / A pseudo-differential calculus on the Heisenberg group. In: Comptes Rendus Mathematique. 2014 ; Vol. 352, No. 3. pp. 197-204.
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