Quaternion linear canonical S-transform and associated uncertainty principles

In this paper, we introduce the notion of quaternion linear canonical S-transform (Q-LOST) which is an extension of the linear canonical S-transform and study the uncertainty principles associated with the Q-LCST. First, we propose the definition of Q-LOST and then study the fundamental properties of Q-LCST including linearity, shift, modulation, orthogonality relation and reconstruction formula. Second, we derive the associated Heisenbergs uncertainty inequality and the corresponding logarithmic version for Q-LCST. Finally, some potential applications of the Q-LCST are introduced.