Pseudo-differential analysis on stratified groups
Lead Research Organisation:
Imperial College London
Department Name: 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.
People |
ORCID iD |
Michael Ruzhansky (Primary Supervisor) | |
Marianna Chatzakou (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509486/1 | 30/09/2016 | 30/03/2022 | |||
1832455 | Studentship | EP/N509486/1 | 30/09/2016 | 30/03/2020 | 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 |