Inverse Strichartz estimates for 1d Schrödinger operators with potentials of quadratic growth

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.

Improved exposition; added figures; added R. Killip and M. Visan as co-authors; 22 pages

References in corpus (2)

• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher