Direct and inverse problems for a periodic problem with non-local\n potential

2020/01/16 by Vladimir A. Zolotarev, Zolotarev, Vladimir A.
Mathematics · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2001.05771

Abstract

Sum of a second derivative operator with periodic boundary conditions and an\nintegral operator of rank one (non-local potential) is studied in this\nmanuscript. Not only spectral analysis is conducted for this operator but the\ninverse problem is solved, viz., a method of the reconstruction of non-local\npotential by the spectral data is presented. Class of spectral data that give\nthe solution to the inverse problem is described.\n

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