Analysis on CR manifolds
Joseph Kohn
Princeton
University
The talk will be concerned
with three dimensional CR manifolds, it will be an introduction to
PDE methods and microlocal analysis on such manifolds. The phenomena
of "loss of derivatives" will be presented, the striking example
phenomenon is the Lewy operator L. This operator has the remarkable
property that for some infinitely differentiable functions f the
equation Lu=f does not solutions in any open set - thus representing
an infinite loss of derivatives. I will discuss examples of
operators which have finite loss of derivatives and are hypoelliptic.