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.
Wiener Tauberian theorem, Paley-Wiener theorem, convolution, asymptotic behavior, Young inequality
CASTRO, LUIS PINHEIRO DE; GUERRA, RITA CORREIA; and TUAN, NGUYEN MINH
"On Wiener's Tauberian theorems and convolution for oscillatory integral operators,"
Turkish Journal of Mathematics: Vol. 43:
3, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/6