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

2015/09/11 by Jao, Casey, Killip, Rowan, Visan, Monica
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.03592

Abstract

We prove inverse Strichartz theorems at L² 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∂_t u = -\tfrac12 Δu. Motivated by applications to the mass-critical Schrödinger equation with external potentials (such as the harmonic oscillator) we use a physical space approach.

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