一维中strstrichartz不等式的一个注释

IF 1.1 3区数学 Q2 MATHEMATICS, APPLIED

Dynamics of Partial Differential Equations Pub Date : 2021-01-04 DOI:10.4310/dpde.2022.v19.n2.a4

R. Frier, Shuanglin Shao

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引用次数: 2

摘要

本文研究了R上Schrödinger方程的Strichartz不等式的极值问题。我们证明了相关的欧拉-拉格朗日方程的解在傅立叶空间中是指数衰减的，因此可以推广为复解析的。因此，我们为极值函数的刻画提供了一个新的证明：唯一的极值是高斯函数，这是Foschi[7]和Hundertmark-Zarnitsky[11]之前研究过的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A remark on the Strichartz inequality in one dimension

In this paper, we study the extremal problem for the Strichartz inequality for the Schrödinger equation on R. 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 [7] and Hundertmark-Zharnitsky [11].

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来源期刊

Dynamics of Partial Differential Equations 数学-应用数学

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes novel results in the areas of partial differential equations and dynamical systems in general, with priority given to dynamical system theory or dynamical aspects of partial differential equations.