The inseparable multi-dimensional quaternion offset linear canonical transform and uncertainty principles

In this paper, we mainly study the definition and properties of the inseparable multi-dimensional offset linear canonical transform for the quaternion-valued functions. First, the (m+n)-dimensional two-sided quaternion offset linear canonical transform is defined by symplectic matrices and the properties including the inversion formula, the Parseval's relation and the convolution theorem are demonstrated. Then, we establish some uncertainty principles (UPs) for the proposed (m+n)-dimensional two-sided quaternion offset linear canonical transform, involving the Heisenberg's UP, logarithmic UP, Donoho-Stark UP and Miyachi's UP.