Erratum for “The Dirac Operator with Mass $m_0 \geq 0$: Non-Existence of Zero Modes and of Threshold Eigenvalues”

Abstract

We give a proof of Theorem 2.1 in [ H. Kalf et al., Doc. Math. 20, 37–64 (2015; Zbl 1333.35227)], namely of the following assertion. Let Q \colon \mathbb{R}^n \rightarrow \mathbb{C}^{N\times N} be measurable with \sup_{x \in \mathbb{R}^n} |x||Q(x)| \leq C \ \ \text{ for some}\ \ 0<C<\frac{n-1}{2}. Then any solution u \in H_{\text{loc}}^1(\mathbb{R}^n)^N \cap L^2(\mathbb{R}^n, r^{-1}dx)^N of (\alpha\cdot p +Q)u=0 is identically zero.