On characterization of the sharp strichartz inequality for the schrödinger equation

Abstract

We study the extremal problem for the Strichartz inequality for the Schrödinger equation on ℝ × ℝ2. 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.