Extensions of the Heisenberg-Weyl inequality (Q1074045)

Summary: A number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove the n-dimensional Hirschman entropy inequality from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality. 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.