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

Takashi Okaji; Osanobu Yamada; Hubert Kalf

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”

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
Hubert Kalf
Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany

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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

Takashi Okaji, Osanobu Yamada, Hubert Kalf, 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