Funções Lq ultradiferenciáveis globais e aplicações

Abstract

The class of global Gevrey functions was introduced recently by Z. Adwan, G. Hoepfner and A. Raich, the elements in these spaces are defined in terms of its derivatives with estimates that depend on sequences. It is know that in the local case ultradifferentiable functions defined by sequences and weight functions are not always the same. In this work we shall introduce the class of global ultradifferentiable functions according with weight functions, making a study from the point of view of functional analysis. It is possible to characterize these classes of functions by decaying of their FBI transform, that is, there exist a version of Paley-Wiener theorem. Our techniques, when adapted to the local case generalize recent results such as the existence of almost analytic extensions. As application, we introduce global ultradifferentiable vectors and show the validity of the global Kotake-Narasimhan theorem in this setting.