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arXiv · 2101.01148

A remark on the Strichartz inequality in one dimension

Ryan Frier·Shuanglin Shao
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Abstract

In this paper, we study the extremal problem for the Strichartz inequality for the Schr\"{o}dinger equation on $\mathbb{R}^2$. We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier space and thus can be extended to be complex analytic. Consequently we provide a new proof to the characterization of the extremal functions: the only extremals are Gaussian functions, which was investigated previously by Foschi and Hundertmark-Zharnitsky.

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Ryan Frier, Shuanglin Shao. 2021-01-04. A remark on the Strichartz inequality in one dimension. https://arxiv.org/abs/2101.01148

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