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.
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Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer, Strichartz inequality for orthonormal functions. J. Eur. Math. Soc. 16 (2014), no. 7, pp. 1507–1526DOI 10.4171/JEMS/467