Differential Equations

, Volume 54, Issue 5, pp 586–595 | Cite as

Dirac Operator with a Potential of Special Form and with the Periodic Boundary Conditions

  • M. Sh. Burlutskaya
  • A. P. Khromov
Ordinary Differential Equations


We consider the Dirac operator on the interval [0, 1] with the periodic boundary conditions and with a continuous potential Q(x) whose diagonal is zero and which satisfies the condition Q(x) = QT(1−x), x ∈ [0, 1]. We establish a relationship between the spectrum of this operator and the spectra of related functional-differential operators with involution. We prove that the system of eigenfunctions of this Dirac operator has the Riesz basis property in the space L 2 2 [0, 1].


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.Saratov State University (National Research University)SaratovRussia

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