Maximal estimates for the Schrödinger equation with orthonormal initial data

• Neal Bez ^[1] ; Sanghyuk Lee ^[2] ; Shohei Nakamura ^[3]
  1. [1] Saitama University

     Saitama University

     Minuma-ku, Japón

     
  2. [2] Seoul National University

     Seoul National University

     Corea del Sur

     
  3. [3] Tokyo Metropolitan University

     Tokyo Metropolitan University

     Japón

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 4, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00582-6
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• Resumen

  • For the one-dimensional Schrödinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates generalize a classical result of Kenig–Ponce–Vega and allow us to obtain pointwise convergence results associated with systems of infinitely many fermions. The maximal-in-space estimates simultaneously address an endpoint problem raised by Frank–Sabin in their work on Strichartz estimates for orthonormal systems of data, and provide a path toward proving our maximal-in-time estimates.