An inverse spectral problem for integro-differential Dirac operators with general convolution kernels. Issue 4 (11th March 2020)

• Record Type: Journal Article
• Authors: Bondarenko, Natalia; Buterin, Sergey
• Is Part Of: Applicable analysis. Volume 99:Issue 4(2020)
• Page Start: 700
• Page End: 716
• Publication Date: 2020-03-11
• Subjects: Yongzhi Xu; Non-selfadjoint Dirac system -- integro-differential operator -- nonlocal operator -- inverse spectral problem -- nonlinear integral equation; 34A55 -- 45J05 -- 34B09 -- 34B10 -- 45G15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1508653
• Languages: English
• ISSNs: 0003-6811

Abstract

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.