9I制作厂免费

Title:聽Fredholm Theory of Non-Elliptic Operators with Trapping.

Abstract:聽In this talk, we will discuss how one shows that a non-elliptic differential operator P is Fredholm on appropriate function spaces. Contrary to the elliptic setting, the Fredholmness of such operators depends on the global properties of the associated classical flow. In the non-trapping case, which roughly corresponds to when the flow has global hyperbolic attractors/repellors with specific properties, the Fredholm theory was obtained on variants of Sobolev spaces. When trapping is present, meaning that some integral curves do not reach these attractors/repellors, P is no longer Fredholm on these function spaces. If the trapping is normally hyperbolic, we will describe a well behaved Fredholm theory, albeit on spaces of distributions with weaker regularity at the unstable manifold of the trapped set. Finally, applications will be given to inverting wave operators on spacetimes.聽