International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 185-192
doi:10.1155/S0161171286000212

Extensions of the Heisenberg-Weyl inequality

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.