Suppose that is a function on such that and are bounded, where . Hardy's Uncertainty Principle asserts that if , then , while if , then . In this paper, we generalise this uncertainty principle to vector-valued functions, and hence to operators. The principle for operators can be formulated loosely by saying that the kernel of an operator cannot be localised near the diagonal if the spectrum is also localised.
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Michael Cowling, Bruno Demange, M. Sundari, Vector-valued distributions and Hardy’s uncertainty principle for operators. Rev. Mat. Iberoam. 26 (2010), no. 1, pp. 133–146DOI 10.4171/RMI/597