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 $ℝ\times {ℝ}^2$. 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.