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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 4
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Articles

An inverse spectral problem for integro-differential Dirac operators with general convolution kernels

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Pages 700-716 | Received 09 Mar 2018, Accepted 31 Jul 2018, Published online: 15 Aug 2018
 

ABSTRACT

An integro-differential Dirac system with a convolution kernel consisting of four independent functions is considered. We prove that the kernel is uniquely determined by specifying the spectra of two boundary value problems with one common boundary condition. The proof is based on the reduction of this nonlinear inverse problem to solving some nonlinear integral equation, which we solve globally. On this basis we also obtain a constructive procedure for solving the inverse problem along with necessary and sufficient conditions for its solvability in an appropriate class of kernels.

COMMUNICATED BY:

AMS MATHEMATICS SUBJECT CLASSIFICATION (2010):

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Grant 17-11-01193 of the Russian Science Foundation.

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