Funding: This research is partly funded by National Nature Science Foundation of China (No. 12401160), the Natural Science Foundation of Shandong Province (Nos. ZR2024MA020 and ZR2023MA023), and the Project of Youth Innovation Team of Universities of Shandong Province (No. 2022KJ314).

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ABSTRACT

In this paper, we identify a class of Dirac equations such that for any Dirac operator problem composed of such an equation and an arbitrary separated or real coupled self-adjoint boundary condition, it can be represented as an equivalent finite dimensional matrix eigenvalue problem. Conversely, given any matrix eigenvalue problem of a specific type and an appropriate separated or real coupled self-adjoint boundary condition, we construct a class of Dirac operators with the specified boundary condition. Each of these Dirac operators is equivalent to the given matrix eigenvalue problem, where equivalence implies that they possess exactly the same eigenvalues.

Conflicts of Interest

The authors declare no conflicts of interest.

Open Research

Data Availability Statement

Data sharing is not applicable to this article.

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Volume48, Issue12

August 2025

Pages 11769-11779

Matrix Representations of Dirac Operators With Finite Spectrum

ABSTRACT

Conflicts of Interest

Open Research

Data Availability Statement

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Matrix Representations of Dirac Operators With Finite Spectrum

ABSTRACT

Conflicts of Interest

Open Research

Data Availability Statement

References

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