Abstract
In this paper, the relation between linear canonical transform (LCT) and quaternion linear canonical transform (QLCT) by using orthogonal plan split (OPS) method is studied. Further, several inequalities like sharp Young–Hausdorff inequality and Pitt's inequality are proved. Moreover, entropy uncertainty principle, sharp local uncertainty principle, and Heisenberg's uncertainty principle for the two‐sided QLCT are also discussed.
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