Strong Unique Continuation for Fractional Schrödinger Operators

We prove the strong unique continuation property for the fractional Schrödinger equation $$(-\mathrm{\Delta }{)}^{s}u=Vu$$ with scaling-critical potentials $V\in L_{\mathrm{l}\mathrm{o}\mathrm{c}}^{\frac{n}{2s}}$ for all $0<s<1$. Our result constitutes the nonlocal counterpart to the classical Jerison–Kenig result for Schrödinger operators.