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Inverse problem for Dirac operators with a constant delay less than half the length of the interval

Đurić Nebojša (Faculty of Electrical Engineering, University of Banja Luka, Bosnia and Herzegovina), nebojsa.djuric@etf.unibl.org
Vojvodić Biljana (Faculty of Mechanical Engineering, University of Banja Luka, Bosnia and Herzegovina), biljana.vojvodic@mf.unibl.org

We study inverse spectral problems for Dirac-type functional-differential operators with a constant delay a ∈ [π/3, π/2).We consider the asymptotic behavior of eigenvalues and research the inverse problem of recovering operators from two spectra. The main result of the paper refers to the proof that the operator could be recovered uniquely from two spectra in the case a ∈ [2π/5, π/2), as well as the proof that it is not possible in the case a ∈ [π/3, 2π/5).

Keywords: Dirac-type operator, Constant delay, Functional-differential operator, Inverse spectral problem