A Paley-Wiener theorem in extended Gevrey regularity
arXiv:1901.00698
Abstract
In this paper we introduce appropriate associated function to the sequence $M_p=p^{\t p^{\s}}$, , $\t>0$, $\s>1$, and derive its sharp asymptotic estimates in terms of the Lambert function. These estimates are used to prove a Paley-Wiener type theorem for compactly supported functions from extended Gevrey classes. As an application, we discuss properties of the corresponding wave front sets.