Geodesic
Uncertainty principles and Calder\'on's formulas for the deformed Hankel $L^2_\alpha$-multiplier operators
Problemy analiza, Tome 13 (2024) no. 3, pp. 3-22

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The main purpose of this paper is to introduce the deformed Hankel $L^2_\alpha$-multiplier operators and to give some new results related to these operators as Plancherel’s, Calderón's reproducing formulas and Heisenberg's, Donoho-Stark's uncertainty principles. Next, using the theory of reproducing kernels, we give best estimates and an integral representation of the extremal functions related to these operators on weighted Sobolev spaces.
Keywords: deformed Hankel transform, Calderón's reproducing formulas, extremal functions, Heisenberg's uncertainty principle, Donoho-Stark's uncertainty principle. 
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     title = {Uncertainty principles and {Calder\'on's} formulas for the deformed {Hankel} $L^2_\alpha$-multiplier operators},
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A. Chana; A. Akhlidj. Uncertainty principles and Calder\'on's formulas for the deformed Hankel $L^2_\alpha$-multiplier operators. Problemy analiza, Tome 13 (2024) no. 3, pp. 3-22. http://geodesic.mathdoc.fr/item/PA_2024_13_3_a0/