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arXiv · 2102.07383

Restriction theorem for the Fourier-Hermite transform and solution of the Hermite-Schr\"odinger equation

Shyam Swarup Mondal·Jitendriya Swain
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Abstract

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 $H=-\Delta+|x|^2$ 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.

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Shyam Swarup Mondal, Jitendriya Swain. 2021-02-15. Restriction theorem for the Fourier-Hermite transform and solution of the Hermite-Schr\"odinger equation. https://arxiv.org/abs/2102.07383

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