Open AccessAn inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions
Author(s) -
Sergey Buterin
Publication year - 2019
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.50.2019.3347
Subject(s) - mathematics , sturm–liouville theory , boundary value problem , robin boundary condition , mathematical analysis , uniqueness , inverse , operator (biology) , differential operator , inverse problem , convolution (computer science) , constructive , type (biology) , perturbation (astronomy) , boundary (topology) , mixed boundary condition , process (computing) , repressor , ecology , chemistry , computer science , biology , operating system , biochemistry , geometry , quantum mechanics , machine learning , artificial neural network , transcription factor , physics , gene
The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.