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.
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In memory of Boris Korenblum
The author was supported by the Göran Gustafsson Foundation (KVA) and by Vetenskapsrådet (VR).
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Hedenmalm, H. Heisenberg’s uncertainty principle in the sense of Beurling. JAMA 118, 691–702 (2012). https://doi.org/10.1007/s11854-012-0048-9
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DOI: https://doi.org/10.1007/s11854-012-0048-9