Strong Unique Continuation for Fractional Schr\"odinger Operators

Abstract

We prove the strong unique continuation property for the fractional Schr\"odinger equation \[ (-\Delta)^s u=Vu \] with scaling-critical potentials $ V\in L^{\frac{n}{2s}}_{\mathrm{loc}}$ for all $0<s<1$. Our result constitutes the nonlocal counterpart to the classical Jerison--Kenig result for Schr\"odinger operators.