Journal of the European Mathematical Society

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Volume 16, Issue 7, 2014, pp. 1507–1526
DOI: 10.4171/JEMS/467

Published online: 2014-08-23

Strichartz inequality for orthonormal functions

Rupert L. Frank[1], Mathieu Lewin[2], Elliott H. Lieb[3] and Robert Seiringer[4]

(1) Caltech, Pasadena, United States
(2) Université de Cergy-Pontoise, France
(3) Princeton University, United States
(4) Institute of Science and Technology Austria, Klosterneuburg, Austria

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.

Keywords: Strichartz inequality for orthonormal functions, dispersive estimates, wave operators, trace ideals

Frank Rupert, Lewin Mathieu, Lieb Elliott, Seiringer Robert: Strichartz inequality for orthonormal functions. J. Eur. Math. Soc. 16 (2014), 1507-1526. doi: 10.4171/JEMS/467