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Strichartz inequality for orthonormal functions

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arxiv 1306.1309 v2 pith:P5RVS5X3 submitted 2013-06-06 math.AP math-phmath.MP

Strichartz inequality for orthonormal functions

Rupert L. Frank , Mathieu Lewin , Elliott H. Lieb , Robert Seiringer This is my paper
classification math.AP math-phmath.MP
keywords inequalityfunctionsstrichartzgeneralizesorthonormalapplicationbehaviorconsider
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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.

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