Extensions of the Heisenberg-Weyl inequality

H. P. Heinig and M. Smith

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-8

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.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:504349

DOI: 10.1155/S0161171286000212

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