Sub-elliptic pseudo-differential calculus on SU(2) and related results

Abstract

This thesis aims to develop a sub-elliptic pseudo-differential calculus on any compact Lie group G. We build an operator class which forms an algebra of operators.

We consider a Hormander system on G and its associated sub-Laplacian L. The Sobolev spaces that arise naturally from the sub-elliptic operator L are well known, and we check some important properties.

Our symbolic calculus is then developed, we define our symbol classes Sm on G and their associated operator classes m, for m R. A particular example of these symbol classes, Sm(Q0), is considered and we show that Sm(Q0) is contained in any Sm.

The core results of this thesis are then proved. We show that if T1 E m1 (Q0) and T2 E m2(Q0), then the composition operator T1 T2 satisfies

T1 T2 E m1+m2(Q0).

Date of Award	23 Mar 2022
Original language	English
Awarding Institution	University of Bath
Supervisor	Veronique Fischer (Supervisor) & Fran Burstall (Supervisor)