Mass-critical inverse Strichartz theorems for 1d Schrödinger operators

Abstract

We prove inverse Strichartz theorems at $L^2$ regularity for a family of Schrödinger evolutions in one space dimension. Prior results rely on spacetime Fourier analysis and are limited to the translation-invariant equation $i{\partial }_{t}u=-\frac{1}{2}\Delta u$. Motivated by applications to the mass-critical Schrödinger equation with external potentials (such as the harmonic oscillator), we use a physical space approach.