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

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:

• Yongzhi Xu

KEYWORDS:

• Non-selfadjoint Dirac system
• integro-differential operator
• nonlocal operator
• inverse spectral problem
• nonlinear integral equation

AMS MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 34A55
• 45J05
• 34B09
• 34B10
• 45G15

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.