Kalf, Hubert; Okaji, Takashi; Yamada, Osanobu

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


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


Dirac operators, virial theorem, threshold eigenvalue, zero mode


  • 1. 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.


Kalf, Hubert
Mathematisches Institut der Universit\``at M\''unchen, Theresienstr. 39, 80333 München, Germany
Okaji, Takashi
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Yamada, Osanobu
Faculty of Science and Engineering, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan