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

摘要

We prove various versions of uncertainty principles for a certain Fourier transform J_A. 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 J_A and relate them to the characterization of the heat kernel corresponding to J_A. Heisenberg's and local uncertainty inequalities are also proved.