Pseudo-differential analysis on stratified groups

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics

Abstract

In aim of the project is to carry out some explicit analysis in the context of stratified groups. The first aim is to extend the pseudo-differential analysis explicitly available on the Heisenberg group to the context of Angel and Cartan groups. This will include explicit expressions for the infinitesimal representations of invariant vector fields and the sub-Laplacian, versions of the Kohn-Nirenberg and Weyl type quantizations, with applications to the analysis of Gevrey spaces and wave type equations. Consequently, one aims at extending this to the setting of more general stratified groups aided by the explicit sights obtained from these specific cases.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 30/09/2021
1832455 Studentship EP/N509486/1 01/10/2016 31/03/2020 Marianna Chatzakou
 
Description We are developing a global pseudo-differential calculus for the Engel and Cartan groups; Lie groups of 3-steps. Moreover, we have studied spectral and continuous properties of the anharmonic oscillator by defining the Hormander class of symbol where the symbol of the anharmonic oscillator belongs to. We are prooving the q-spectral gap Poincre inequality in the setting of the Engel and the Cartan group.
Exploitation Route The anharmonic oscillator is an important operator that appears in quantum physics.
Sectors Education

URL https://www.researchgate.net/publication/329206432_On_a_class_of_anharmonic_oscillators
 
Description Work on the anharamonic oscillator 
Organisation Queen Mary University of London
Country United Kingdom 
Sector Academic/University 
PI Contribution we investigated the Hormander classes associated with the anharmonic oscillator
Collaborator Contribution My partner helped me in understanding the Hormander classes of symbols
Impact We submitted a paper for possible publication to the Journal Communications in Mathematical Physics
Start Year 2018