Quaternion linear canonical<i>S</i>-transform and associated uncertainty principles
M. Younus BhatDepartment of Mathematical Sciences, Islamic University of Science and Technology Kashmir, IndiaAamir H. DarDepartment of Mathematical Sciences, Islamic University of Science and Technology Kashmir, India
2022en
ABI
Abstract
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.
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