Strichartz inequality for orthonormal functions
Analysis of PDEs
2014-11-07 v2 Mathematical Physics
math.MP
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 Schr\"odinger equation in a time-dependent potential and we show the existence of the wave operator in Schatten spaces.
Cite
@article{arxiv.1306.1309,
title = {Strichartz inequality for orthonormal functions},
author = {Rupert L. Frank and Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
journal= {arXiv preprint arXiv:1306.1309},
year = {2014}
}
Comments
Final version to appear in the Journal of the European Mathematical Society