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

Hubert Kalf; Takashi Okaji; Osanobu Yamada

doi:10.4171/dm/706

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

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

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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 $Q : R^{n} \to C^{N \times N}$ be measurable with

x \in R^{n} sup ∣ x ∣∣ Q (x) ∣ \leq C for some 0 < C < \frac{n - 1}{2} .

Then any solution $u \in H_{loc}^{1} (R^{n})^{N} \cap L^{2} (R^{n}, r^{- 1} d x)^{N}$ of $(α \cdot p + Q) u = 0$ is identically zero.

Link to the paper corrected hereby.

Cite this article

Hubert Kalf, Takashi Okaji, Osanobu Yamada, Erratum for “The Dirac Operator with Mass $m_{0} \geq 0$ : Non-Existence of Zero Modes and of Threshold Eigenvalues”. Doc. Math. 24 (2019), pp. 1361–1363

DOI 10.4171/DM/706