#### Vol. 9, No. 2, 2016

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On characterization of the sharp Strichartz inequality for the Schrödinger equation

### Jin-Cheng Jiang and Shuanglin Shao

Vol. 9 (2016), No. 2, 353–361
##### Abstract

We study the extremal problem for the Strichartz inequality for the Schrödinger equation on $ℝ×{ℝ}^{2}$. 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 of the characterization of the extremal functions: the only extremals are Gaussian functions, as investigated previously by Foschi, Hundertmark and Zharnitsky.

##### Keywords
Schrödinger equation, Strichartz inequality and extremals
Primary: 35J10