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On characterization of
the sharp Strichartz inequality for the Schrödinger
equation
Jin-Cheng Jiang and Shuanglin Shao |
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Vol. 9 (2016), No. 2, 353–361
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Abstract |
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We study the extremal problem for the Strichartz inequality for the Schrödinger equation on . 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
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Mathematical Subject Classification 2010
Primary: 35J10
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Milestones
Received: 22 April 2014
Revised: 28 September 2015
Accepted: 16 December 2015
Published: 24 March 2016
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Authors |
| Jin-Cheng Jiang | |
| Department of Mathematics National Tsing-Hua University No. 101, Section 2, Kuang-Fu Road Hsinchu 30013 Taiwan |
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| Shuanglin Shao | |
| Department of Mathematics University of Kansas 615 Snow Hall 1460 Jayhawk Blvd Lawrence, KS 66045-7594 United States |
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