A Paley-Wiener theorem in extended Gevrey regularity
Abstract
In this paper we introduce appropriate associated function to the sequence Mp=p p, p∈ , >0, >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.
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