On Wiener’s Tauberian theorems and convolution for oscillatory integral operators

Abstract

The main aim of this work is to obtain Paley–Wiener and Wiener’s Tauberian results associated withan oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent newconvolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-typealgebra is also associated with this convolution.