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 × 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
Mathematical Subject Classification 2010
Primary: 35J10
Milestones
Received: 22 April 2014
Revised: 28 September 2015
Accepted: 16 December 2015
Published: 24 March 2016
Authors
Jin-Cheng Jiang
Department of Mathematics
National Tsing-Hua University
No. 101, Section 2, Kuang-Fu Road
Hsinchu 30013
Taiwan
Shuanglin Shao
Department of Mathematics
University of Kansas
615 Snow Hall
1460 Jayhawk Blvd
Lawrence, KS 66045-7594
United States