Quaternion linear canonicalS-transform and associated uncertainty principles

In this paper, we introduce the notion of quaternion linear canonical S-transform (Q-LCST) 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-LCST and then study the fundamental properties of [Formula: see text]-LCST including linearity, shift, modulation, orthogonality relation and reconstruction formula. Second, we derive the associated Heisenbergs uncertainty inequality and the corresponding logarithmic version for [Formula: see text]-LCST. Finally, some potential applications of the Q-LCST are introduced.