Research Information System
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol.25, no.10, pp.1508-1518, 2017 (SCI-Expanded)
We consider the Sturm-Liouville differential operator on a finite interval with Dirichlet boundary conditions perturbed with a convolution integral operator. The inverse problem is studied of recovering the convolution kernel from a half spectrum, provided that the kernel function on the first half of the interval as well as the Sturm-Liouville potential on the entire interval are known a priori. Besides the uniqueness of a solution of this half inverse problem, we also obtain necessary and sufficient conditions of its solvability. A constructive procedure for solving the inverse problem is also provided.