Schrödinger operators with Highly Singular, Oscillating Potentials.
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Karl-Theodor Sturm (1992)
Manuscripta mathematica
Armin Kargol (1999)
Annales de l'I.H.P. Physique théorique
Justin Holmer, Jeremy Marzuola, Maciej Zworski (2006)
Journées Équations aux dérivées partielles
Matthias Hübner, Herbert Spohn (1995)
Annales de l'I.H.P. Physique théorique
Rupert Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer (2014)
Journal of the European Mathematical Society
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.
A. Martinez (1994/1995)
Séminaire Équations aux dérivées partielles (Polytechnique)
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