The gyrator transform of the generalized functions

The gyrator transform is an integral transform that has attracted much attention in the field of optics and other engineering fields. We consider the image of the gyrator transform of the Gelfand-Shilov space and its dual space. While the gyrator transform is closely related to the fractional Fourier transform, we discuss the difference between these two transforms. Moreover, we show the relation between the above spaces and the eigenfunctions of the gyrator transform.