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Article Dans Une Revue Advances in Pure and Applied Mathematics Année : 2015

Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators

Résumé

We prove various versions of uncertainty principles for a certain Fourier transform $\mathcal F_A.$ Here $A$ is a Chébli function (i.e. a Sturm-Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of type Gelfand-Shilov, Morgan's, Hardy's, and Cowling-Price, for $\mathcal F_A,$ and relating them to the characterization of the heat kernel corresponding to $\mathcal F_A.$ Heisenberg's and local uncertainty inequalities were also proved.
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Dates et versions

hal-01282492 , version 1 (03-03-2016)

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Salem Ben Saïd, Asma Boussen, Mohamed Sifi. Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators. Advances in Pure and Applied Mathematics, 2015, 6 (4), pp.215-239. ⟨10.1515/apam-2015-5010⟩. ⟨hal-01282492⟩
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