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 with a time-dependent potential and we show the existence of the wave operator in Schatten spaces.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
- Dispersive estimates
- Strichartz inequality for orthonormal functions
- Trace ideals
- Wave operators