Beyond Gevrey Regularity: Superposition and Propagation of Singularities

Abstract

We propose a relaxation of Gevrey regularity condition
by using sequences which depend on two parameters and
define families of ultradifferentiable functions which contain
Gevrey classes. It is shown that such families
are closed under superposition, and therefore inverse closed as well.
Furthermore, we study partial differential operators
whose coefficients are less regular then Gevrey-type ultradifferentiable functions.
To that aim we introduce appropriate wave front sets and prove a theorem on propagation of singularities.
This extends related known results in the sense that assumptions on the regularity of
the coefficients are weakened.