Uniform stability of the inverse spectral problem for a convolution integro-differential operator

Abstract

The operator of double differentiation perturbed by the composition of the differentiation operator and a convolution one on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the convolution kernel from the spectrum both in a weighted L2-norm and in a weighted uniform norm. For this purpose, we successively prove uniform stability of each step of the algorithm for solving this inverse problem in both norms. The obtained results reveal some essential difference from the classical inverse Sturm–Liouville problem.