Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform
Received:March 01, 2021  Revised:May 20, 2021
Key Word: Laeng-Morpurgo-type inequality   local-type inequality   Heisenberg-Pauli-Weyl-type inequality  
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Author NameAffiliation
Fethi SOLTANI Facult\'e des Sciences de Tunis, Laboratoire d'Analyse Math\'ematique et Applications LR11ES11, Universit\'e de Tunis El Manar, Tunis 2092, Tunisia
Ecole Nationale d'Ing\'enieurs de Carthage, Universit\'e de Carthage, Tunis 2035, Tunisia 
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      In this work, we prove Clarkson-type and Nash-type inequalities for the Laguerre transform $\mathfrak{F}_L$ on $\mathbb{M}=[0, \infty) \times \mathbb{R}$. By combining these inequalities, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also a local-type uncertainty inequalities for the Laguerre transform $\mathfrak{F}_L$, and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.
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