JournalsjemsVol. 10, No. 4pp. 883–907

Hardy's uncertainty principle, convexity and Schrödinger evolutions

  • Luis Escauriaza

    Universidad del Pais Vasco, Bilbao, Spain

  • Carlos E. Kenig

    University of Chicago, USA

  • Gustavo Ponce

    University of California, Santa Barbara, USA

  • Luis Vega

    Universidad del Pais Vasco, Bilbao, Spain
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Abstract

We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schrödinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy's version of the uncertainty principle. We also obtain corresponding results for heat evolutions.

Cite this article

Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce, Luis Vega, Hardy's uncertainty principle, convexity and Schrödinger evolutions. J. Eur. Math. Soc. 10 (2008), no. 4, pp. 883–907

DOI 10.4171/JEMS/134