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

Kalf, Hubert ; Okaji, Takashi ; Yamada, Osanobu

Documenta mathematica, Tome 24 (2019), pp. 1361-1363.

Résumé

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$

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.

Détail

Classification : 35P15, 81Q10, 35Q41, 81Q05
Keywords: Dirac operators, virial theorem, threshold eigenvalue, zero mode