article

Title: Unique continuation for the Schroedinger equation with potentials in Wiener amalgam spaces

Authors: Ihyeok Seo

Issue: Volume 60 (2011), Issue 4, 1203-1228

Abstract:

$Recently, Cordero and Nicola [E. Cordero and F. Nicola, \textit{Some new Strichartz estimates for the Schr\"odinger equation}, J. Differential Equations \textbf{245} (2008), no. 7, 1945--1974] obtained inhomogeneous Strichartz estimates in Wiener amalgam spaces for the Schr\"odinger equation. In this paper we extend these estimates to a wider range for which the usual estimate ([D. Foschi, \textit{Inhomogeneous Strichartz estimates}, J. Hyperbolic Differ. Equ. \textbf{2} (2005), no. 1, 1--24], [M.C. Vilela, \textit{Inhomogeneous Strichartz estimates for the Schr\"odinger equation}, Trans. Amer. Math. Soc. \textbf{359} (2007), no. 5, 2123--2136]) in Lebesgue spaces is known to hold. This enables us to establish new Carleman estimates which are closely related to the extended estimates. Then we apply them to obtain new results on unique continuation for the Schr\"odinger equation with potentials in Wiener amalgam spaces.$