  The perturbation of the Sturm-Liouville operator on a finite interval with
Dirichlet boundary conditions by a convolution operator is considered. Local
stability and global unique solvability of the inverse problem of recovering
the convolution kernel from the spectrum, provided that the potential is given
a priori, is known. In the present work, we establish uniform full stability of
this inverse problem involving a uniform estimate of deviations of the
convolution kernel via deviations of the spectrum and the potential within
balls of any fixed radii.
