doiSerbia

Beyond gevrey regularity: Superposition and propagation of singularities

Pilipović Stevan (Department of Mathematics and Informatics, University of Novi Sad, Novi Sad)
Teofanov Nenad (Department of Mathematics and Informatics, University of Novi Sad, Novi Sad)
Tomić Filip (Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia)

We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is 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.

Keywords: Gevrey classes, ultradifferentiable functions, wave front sets

Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174024