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 with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.