Extensions of the Heisenberg-Weyl inequality. (English) Zbl 0589.42009

Heinig, H. P.; Smith, M.

Int. J. Math. Math. Sci. 9, 185-192 (1986).

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.

MSC:

42A38	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
26D10	Inequalities involving derivatives and differential and integral operators

Keywords:

Heisenberg-Weyl uncertainty inequality; Hirschman entropy; Hausdorff- Young theorem; weighted entropy inequality