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 with a time-dependent potential and we show the existence of the wave operator in Schatten spaces.
Original language | English (US) |
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Pages (from-to) | 1507-1526 |
Number of pages | 20 |
Journal | Journal of the European Mathematical Society |
Volume | 16 |
Issue number | 7 |
DOIs | |
State | Published - 2014 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
Keywords
- Dispersive estimates
- Strichartz inequality for orthonormal functions
- Trace ideals
- Wave operators