Strichartz inequality for orthonormal functions

Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer

Research output: Contribution to journalArticle

12 Scopus citations

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 languageEnglish (US)
Pages (from-to)1507-1526
Number of pages20
JournalJournal of the European Mathematical Society
Volume16
Issue number7
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Dispersive estimates
  • Strichartz inequality for orthonormal functions
  • Trace ideals
  • Wave operators

Fingerprint Dive into the research topics of 'Strichartz inequality for orthonormal functions'. Together they form a unique fingerprint.

  • Cite this

    Frank, R. L., Lewin, M., Lieb, E. H., & Seiringer, R. (2014). Strichartz inequality for orthonormal functions. Journal of the European Mathematical Society, 16(7), 1507-1526. https://doi.org/10.4171/JEMS/467