2010/05/05 by Hajer Bahouri, Clotilde Fermanian Kammerer, Bahouri, Hajer +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations
paper · doi:10.48550/arxiv.1005.0833
openalex publication_date 2010/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on Sobolev spaces and the loss of derivatives may be controled by the order of the operator. Although a large number of works have been devoted in the past to the construction and the study of algebras of variable-coefficient operators, including some very interesting works on the Heisenberg group, our approach is different, and in particular puts into light microlocal directions and completes, with the Littlewood-Paley theory developed in \citebgx and \citebg, a microlocal analysis of the Heisenberg group.