On unique continuation for Schrödinger operators of fractional and higher orders

In this note we study the property of unique continuation for solutions of $|(-Δ)^{α/2}u|\leq|Vu|$, where $V$ is in a function class of potentials including $\bigcup_{p>n/α}L^p(\mathbb{R}^n)$ for $n-1\leqα<n$. In particular, when $n=2$, our result gives a unique continuation theorem for the fractional ($1<α<2$) Schrödinger operator $(-Δ)^{α/2}+V(x)$ in the full range of $α$ values.

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