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Direct and inverse spectral problems for Dirac systems with nonlocal potentials

Dębowska Kamila, Nizhnik Leonid P.

Opuscula Mathematica

2019

Vol. 39, no. 5

645--673

The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on information about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.