Strichartz inequality for orthonormal functions
Rupert L. FrankCaltech, Pasadena, United States
Mathieu LewinUniversité de Cergy-Pontoise, France
Elliott H. LiebPrinceton University, United States
Robert SeiringerInstitute 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.
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. 1507–1526DOI 10.4171/JEMS/467