JournalsjemsVol. 16, No. 7pp. 1507–1526

Strichartz inequality for orthonormal functions

  • Rupert L. Frank

    Caltech, Pasadena, United States

  • Mathieu Lewin

    Université de Cergy-Pontoise, France

  • Elliott H. Lieb

    Princeton University, United States

  • Robert Seiringer

    Institute of Science and Technology Austria, Klosterneuburg, Austria
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Abstract

We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation in a time-dependent potential and we show the existence of the wave operator in Schatten spaces.

Cite this article

Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer, Strichartz inequality for orthonormal functions. J. Eur. Math. Soc. 16 (2014), no. 7, pp. 1507–1526

DOI 10.4171/JEMS/467