Extensions of the Heisenberg-Weyl inequality

Extensions of the Heisenberg-Weyl inequality

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)...

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Bibliographic Details
Main Authors: H. P. Heinig, M. Smith
Format: Article
Language:English
Published: Hindawi Limited 1986-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
uncertainty inequality
Fourier transform
variance
entropy Hausdorff-Young inequality
weighted norm inequalities.
Online Access:http://dx.doi.org/10.1155/S0161171286000212
Description
Summary: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.
ISSN:0161-1712
1687-0425

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