Hardy Uncertainty Principle and unique continuation properties of covariant Schrodinger flows

TL;DR

This paper establishes a Hardy uncertainty principle-inspired unique continuation property for electromagnetic Schrödinger equations by proving a logarithmic convexity result for weighted norms without smallness assumptions on the magnetic potential.

Contribution

It introduces a new logarithmic convexity approach for electromagnetic Schrödinger equations that extends previous unique continuation results without small magnetic potential assumptions.

Findings

Proves a logarithmic convexity result for weighted $L^2$-norms.

Derives a Hardy uncertainty principle-style unique continuation theorem.

Generalizes recent theorems by Escauriaza, Kenig, Ponce, and Vega.

Abstract

We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega.