A Paley–Wiener theorem in extended Gevrey regularity

Abstract

© 2019, Springer Nature Switzerland AG. In this paper we introduce appropriate associated function to the sequence Mp=pτpσ,p∈N,τ>0,σ>1, and derive its sharp asymptotic estimates in terms of the Lambert W 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.