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On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

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Abstract

In this paper we define a one-dimensional discrete Dirac operator on \({\mathbb {Z}}\). We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on \({\mathbb {Z}}\). That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole \({\mathbb {Z}}\).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Artem Hulko

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  1. Artem Hulko
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Correspondence to Artem Hulko.

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The author declares that there is no conflict of interest of any kind.

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Author expresses his gratitude to Dr. Oleg Safronov for his suggestions and remarks.

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Hulko, A. On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential. Anal.Math.Phys. 9, 639–654 (2019). https://doi.org/10.1007/s13324-018-0222-z

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