A pseudo-differential calculus on the Heisenberg group

Veronique Fischer; Michael Ruzhansky

doi:10.1016/j.crma.2013.12.006

A pseudo-differential calculus on the Heisenberg group

Veronique Fischer, Michael Ruzhansky

Imperial College London

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21 Citations (SciVal)

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 language	English
Pages (from-to)	197-204
Journal	Comptes Rendus Mathematique
Volume	352
Issue number	3
Early online date	3 Feb 2014
DOIs	https://doi.org/10.1016/j.crma.2013.12.006
Publication status	Published - Mar 2014

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10.1016/j.crma.2013.12.006

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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.",

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AB - 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.

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JO - Comptes Rendus Mathematique

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A pseudo-differential calculus on the Heisenberg group

Abstract

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