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Restriction theorem for the Fourier-Hermite transform and solution of the Hermite-Schrödinger equation

In this article, we prove the restriction theorem for the Fourier-Hermite transform and obtain the Strichartz estimate for the system of orthonormal functions for the Hermite operator $H=-Δ+|x|^2$ on $\mathbb{R}^n$ as application. Further, we show the an optimal behavior of the constant in the Strichartz estimate as limit of a large number of functions.