On unique continuation for Schrödinger operators of fractional and higher orders

Abstract

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

Revised version, to appear in Mathematische Nachrichten

References in corpus (1)

• Fractional Quantum Mechanics

Cited by in corpus (3)

• Unique Continuation for Fractional Schrödinger Equations with Rough Potential
• Unique continuation for fractional Schrödinger operators in three and higher dimensions
• Carleman inequalities for fractional Laplacians and unique continuation