Generalized Uncertainty Principles associated with the Quaternionic Offset Linear Canonical Transform

The quaternionic offset linear canonical transform (QOLCT) can be thought as a generalization of the quaternionic linear canonical transform (QLCT). In this paper we define the QOLCT, we derive the relationship between the QOLCT and the quaternion Fourier transform (QFT). Based on this fact we prove the Plancherel formula, and some properties related to the QOLCT, then we generalize some different uncertainty principles (UPs), including Heisenberg-Weyls UP, Hardys UP, Beurlings UP, and logarithmic UP to the QOLCT domain in a broader sense