Strichartz inequality for orthonormal functions
Rupert L. Frank
Caltech, Pasadena, United StatesMathieu Lewin
Université de Cergy-Pontoise, FranceElliott H. Lieb
Princeton University, United StatesRobert Seiringer
Institute of Science and Technology Austria, Klosterneuburg, Austria
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