UNCERTAINTY PRINCIPLES AND CALDER ´ON’S FORMULAS FOR THE DEFORMED HANKEL 𝐿^2_𝛼-MULTIPLIER OPERATORS by A. Chana, A. Akhlidj

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On Some Inequalities of Uncertainty Principles Type in Quantum Calculus by Ahmed Fitouhi, Néji Bettaibi, Rym H. Bettaieb, Wafa Binous

“…The aim of this paper is to generalize the 𝑞-Heisenberg uncertainty principles studied by Bettaibi et al. (2007), to state local uncertainty principles for the 𝑞-Fourier-cosine, the 𝑞-Fourier-sine, and the 𝑞-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the 𝑞-Bessel-Fourier transform.…”
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A Possible Solution of the Cosmological Constant Problem Based on GW170817 and Planck Observations with Minimal Length Uncertainty by Abdel Magied Diab, Abdel Nasser Tawfik

“…Utilizing features of the UV/IR correspondence and the apparent similarities between GUP (including nongravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant Λ (obviously manifesting gravitational influences on the vacuum energy density), known as catastrophe of nongravitating vacuum, we suggest a possible solution for this long-standing physical problem, Λ≃10−47 GeV4/ℏ3c3.…”
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Discreteness of Curved Spacetime from GUP by Ahmad Adel Abutaleb

“…Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP). …”
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Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras by Firdous A. Shah, Aajaz A. Teali, Mawardi Bahri

“…We culminated our investigation by deriving several uncertainty principles such as the Heisenberg–Pauli–Weyl uncertainty inequality, Pitt’s inequality, and logarithmic and local-type uncertainty inequalities for the Clifford-valued shearlet transform.…”
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Best approximation of Hartley-Bessel multiplier operators on weighted Sobolev spaces by Ahmed Chana, Abdellatif Akhlidj

“… The main goal of this paper is to introduce the Hartley-Bessel \(L^2_\alpha\)-multiplier operators and to give for them some new results as Plancherel’s, Calderon’s reproducing formulas and Heisenberg’s, Donoho-Stark’s uncertainty principles. …”
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A Convolution-Based Shearlet Transform in Free Metaplectic Domains by Tarun K. Garg, Waseem Z. Lone, Firdous A. Shah, Hatem Mejjaoli

“…Towards the culmination, we formulate the Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform.…”
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