Eigenfunctions of the multidimensional nonseparable linear canonical transform

The eigenfunctions of one and two dimensional linear canonical transform have been investigated in detail. In this paper, we extend these works and derive the eigenfunctions of multidimensional nonseparable linear canonical transform, and the multidimensional nonseparable linear canonical transform is investigated. Since many optical systems can be represented by the LCT, our results will be useful in signal analysis and optics.