We prove various versions of uncertainty principles for a certain Fourier transform FA. Here, A is a Chébli function (that is, a Sturm-Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of Gelfand-Shilov type, of Morgan type, of Hardy type, and of Cowling-Price type, for FA and relate them to the characterization of the heat kernel corresponding to FA. Heisenberg's and local uncertainty inequalities are also proved.
- Differential-reflection operators
- heat kernel
- uncertainty principles
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