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

Authors: LUIS PINHEIRO DE CASTRO, RITA CORREIA GUERRA, NGUYEN MINH TUAN

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.

Keywords: Wiener Tauberian theorem, Paley-Wiener theorem, convolution, asymptotic behavior, Young inequality

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