A pseudo-differential calculus on the Heisenberg group

2014/02/03 by Véronique Fischer, Veronique Fischer, Michael Ruzhansky
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebra over a field #Calculus (dental) #Differential operator #Geometry #Group (periodic table) #Heisenberg group #Lie group #Mathematical Analysis and Transform Methods #Mathematics #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #math.AP #math.FA #math.RT #msc:35S05 #msc:43A80

paper · pdf · doi:10.1016/j.crma.2013.12.006

published as Comptes Rendus Mathematique, Vol. 352, Issue 3, March 2014, pp 197-204 · 9 pages

openalex publication_date 2014/02/03 · arxiv created 2014/02/26 · arxiv updated 2014/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
• Phase-space analysis and pseudodifferential calculus on the Heisenberg group
• Sharp Gårding inequality on compact Lie groups