JournalsjemsVol. 10 , No. 4DOI 10.4171/jems/134

Hardy's uncertainty principle, convexity and Schrödinger evolutions

  • Carlos E. Kenig

    University of Chicago, USA
  • Luis Vega

    Universidad del Pais Vasco, Bilbao, Spain
  • Luis Escauriaza

    Universidad del Pais Vasco, Bilbao, Spain
  • Gustavo Ponce

    University of California, Santa Barbara, USA
Hardy's uncertainty principle, convexity and Schrödinger evolutions cover

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 Schr\"odinger 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.