@article{article_1068024, title={A Note on Function Spaces with Fractional Fourier Transforms in Wiener-type Spaces}, journal={Duzce University Journal of Science and Technology}, volume={11}, pages={717–728}, year={2023}, DOI={10.29130/dubited.1068024}, author={Toksoy, Erdem}, keywords={Fractional Fourier transform, convolution, Wiener-type spaces}, abstract={The purpose of this paper is to introduce and study a function space A_(α,w)^(B,Y) (R^d ) to be a linear space of functions h∈L_w^1 (R^d ) whose fractional Fourier transforms F_α h belong to the Wiener-type space W(B,Y)(R^d ), where w is a Beurling weight function on R^d. We show that this space becomes a Banach algebra with the sum norm 〖‖h‖〗_(1,w)+〖‖F_α h‖〗_(W(B,Y)) and Θ convolution operation under some conditions. We find an approximate identity in this space and show that this space is an abstract Segal algebra with respect to L_w^1 (R^d ) under some conditions.}, number={2}, publisher={Duzce University}