Uncertainty principles associated with quaternion linear canonical transform and their estimates
Manab Kundu, Akhilesh Prasad
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.
Topics & Concepts
MathematicsUncertainty principleQuaternionHausdorff spaceApplied mathematicsEntropy (arrow of time)Linear inequalityMathematical analysisInequalityPure mathematicsGeometryQuantumQuantum mechanicsPhysicsMathematical Analysis and Transform MethodsDigital Filter Design and ImplementationAlgebraic and Geometric Analysis