A variation on uncertainty principles for quaternion linear canonical transform. (English) Zbl 1470.42011
Summary: In this paper we prove Clarkson-type and Nash-type inequalities in the (right-sided) Quaternion Linear Canonical transform (QLCT) for \(L^p\)-functions. Next, we show Heisenberg-type inequalities and Matolcsi-Szücs-type inequality for the QLCT. Finally, we deduce local-type uncertainty inequalities for the Quaternion Linear Canonical transform.
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 44A35 | Convolution as an integral transform |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 34B30 | Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) |
Keywords:
quaternion linear canonical transform; Nash-type inequality; Clarkson-type inequality; Heisenberg-Pauli-Weyl inequalities; Matolcsi-Szücs-type inequality; local-type inequalitiesReferences:
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