Abstract
In this paper a number of generalizations of the classical Heisenberg‐Weyl uncertainty inequality are given. We prove the n‐dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff‐Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2). From a general weighted form of the Hausdorff‐Young theorem, a one‐dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg‐Weyl inequalities are given.
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More From: International Journal of Mathematics and Mathematical Sciences
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