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

International audienceWe 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