Premium
An inverse problem for an integro‐differential operator on a star‐shaped graph
Author(s) -
Bondarenko Natalia P.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4698
Subject(s) - mathematics , inverse problem , constructive , graph , differential operator , inverse , operator (biology) , discrete mathematics , pure mathematics , mathematical analysis , biochemistry , chemistry , geometry , repressor , transcription factor , gene , process (computing) , computer science , operating system
A partial inverse problem for an integro‐differential Sturm‐Liouville operator on a star‐shaped graph is studied. We suppose that the convolution kernels are known on all the edges of the graph except one and recover the kernel on the remaining edge from a part of the spectrum. We prove the uniqueness theorem for this problem and develop a constructive algorithm for its solution, based on the reduction of the inverse problem on the graph to the inverse problem on the interval by using the Riesz basis property of the special system of functions.