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

##### Doc. Math. 24, 1361-1363 (2019)
DOI: 10.25537/dm.2019v24.1361-1363

### Summary

We give a proof of Theorem 2.1 in [\textit{H. Kalf} et al., Doc. Math. 20, 37--64 (2015; Zbl 1333.35227)], namely of the following assertion. \par 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.

### Mathematics Subject Classification

35P15, 81Q10, 35Q41, 81Q05

### Keywords/Phrases

Dirac operators, virial theorem, threshold eigenvalue, zero mode

### References

• [KOY]. Kalf, H., Okaji, T. and Yamada, O., The Dirac operator with mass $m_0 \geq 0$ : Non-existence of zero modes and of threshold eigenvalues, Documenta Math., 20 (2015), 37-64. https://www.elibm.org/article/10000399; zbl 1333.35227; MR3398708.

### Affiliation

Kalf, Hubert
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
Okaji, Takashi
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan