A remark on the Strichartz inequality in one dimension

Abstract

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].