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Hardy Uncertainty Principle, Convexity and Parabolic Evolutions

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Abstract

We give a new proof of the L 2 version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time.We extend the result to heat equations with lower order variable coefficient.

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Authors and Affiliations

  1. Dpto. de Matemáticas, UPV/EHU, Apto. 644, 48080, Bilbao, Spain

    L. Escauriaza & L. Vega

  2. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    C. E. Kenig

  3. Department of Mathematics, University of California, Santa Barbara, CA, 93106, USA

    G. Ponce

Authors
  1. L. Escauriaza
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  2. C. E. Kenig
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  3. G. Ponce
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  4. L. Vega
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Corresponding author

Correspondence to L. Escauriaza.

Additional information

L. Escauriaza and L. Vega are supported by the Grants MTM2014-53145-P and IT641-13 (GIC12/96), C. E. Kenig by NSF Grants DMS-0968472 and DMS-1265249. L. Vega is also supported by SEV-2013-0323.

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Escauriaza, L., Kenig, C.E., Ponce, G. et al. Hardy Uncertainty Principle, Convexity and Parabolic Evolutions. Commun. Math. Phys. 346, 667–678 (2016). https://doi.org/10.1007/s00220-015-2500-z

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  • DOI: https://doi.org/10.1007/s00220-015-2500-z

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