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Inverse spectral problem for the operators with non‐local potential
Author(s) -
Zolotarev Vladimir A.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700029
Subject(s) - mathematics , interlacing , operator (biology) , inverse problem , degenerate energy levels , mathematical analysis , inverse , self adjoint operator , perturbation (astronomy) , interval (graph theory) , boundary value problem , spectral radius , eigenvalues and eigenvectors , hilbert space , combinatorics , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , computer science , transcription factor , gene , operating system
The main object under consideration in the paper is the second derivative operator on a finite interval with zero boundary conditions perturbed by a self‐adjoint integral operator with the degenerate kernel (non‐local potential). The inverse problem, i.e., the reconstruction of the perturbation from the spectral data, is solved by means of the step‐by‐step procedure based on the n ‐interlacing property of the spectrum.