Erratum for "The Dirac Operator with Mass m00m_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
Erratum for "The Dirac Operator with Mass $m_0 \geq 0$: Non-Existence of Zero Modes and of Threshold Eigenvalues" cover
Download PDF

This article is published open access.

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 ⁣:RnCN×NQ \colon \mathbb{R}^n \rightarrow \mathbb{C}^{N\times N} be measurable with supxRnxQ(x)C   for some  0<C<n12.\sup_{x \in \mathbb{R}^n} |x||Q(x)| \leq C \ \ \text{ for some}\ \ 0<C<\frac{n-1}{2}. Then any solution uHloc1(Rn)NL2(Rn,r1dx)Nu \in H_{\text{loc}}^1(\mathbb{R}^n)^N \cap L^2(\mathbb{R}^n, r^{-1}dx)^N of (αp+Q)u=0(\alpha\cdot p +Q)u=0 is identically zero.

Cite this article

Hubert Kalf, Takashi Okaji, Osanobu Yamada, Erratum for "The Dirac Operator with Mass m00m_0 \geq 0: Non-Existence of Zero Modes and of Threshold Eigenvalues". Doc. Math. 24 (2019), pp. 1361–1363

DOI 10.4171/DM/706