The Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the Wigner Distribution; Relation With the Notion of Symplectic Capacity

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dc.creatorde Gosson, Maurice
dc.creatorLuef, Franz
dc.date2008-03-06
dc.date.accessioned2026-07-07T09:25:15Z
dc.date.available2026-07-07T09:25:15Z
dc.descriptionWe extend Hardy's uncertainty principle for a square integrable function and its Fourier transform to the multidimensional case using a symplectic diagonalization. We use this extension to show that Hardy's uncertainty principle is equivalent to a statement on the Wigner distribution of the function. We give a geometric interpretation of our results in terms of the notion of symplectic capacity of an ellipsoid. Furthermore, we show that Hardy's uncertainty principle is valid for a general Lagrangian frame of the phase space. Finally, we discuss an extension of Hardy's theorem for the Wigner distribution for exponentials with convex exponents.
dc.identifierhttps://arxiv.org/abs/0803.0910
dc.identifierhttp://arxiv.org/abs/0803.0910
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156341
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectNA
dc.titleThe Multi-Dimensional Hardy Uncertainty Principle and its Interpretation in Terms of the Wigner Distribution; Relation With the Notion of Symplectic Capacity
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