Opuscula Math. 39, no. 5 (2019), 645-673
https://doi.org/10.7494/OpMath.2019.39.5.645

Opuscula Mathematica

# Direct and inverse spectral problems for Dirac systems with nonlocal potentials

Kamila Dębowska
Leonid P. Nizhnik

Abstract. 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 informations 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.

Keywords: inverse spectral problem, nonlocal potential, nonlocal boundary conditions, Dirac system.

Mathematics Subject Classification: 47A75, 34A55, 34B10.

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• Leonid P. Nizhnik
• NASU Institute of Mathematics, Department of Functional Analysis, Tereschenkivska Str. 3, 01 601 Kiev, Ukraine
• Communicated by Alexander Gomilko.
• Revised: 2019-06-11.
• Accepted: 2019-06-17.
• Published online: 2019-09-05.