, Volume 118, Issue 2, pp 691-702
Date: 30 Nov 2012

Heisenberg’s uncertainty principle in the sense of Beurling

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Abstract

We shed new light on Heisenberg’s uncertainty principle in the sense of Beurling, by offering a fundamentally different proof which allows us to weaken the assumptions rather substantially. The new formulation is pretty much optimal, as can be seen from examples. Our arguments involve Fourier and Mellin transforms. We also introduce a version which applies to two given functions. Finally, we show how our approach applies in the higher dimensional setting.