Inverse problem for integral operators

TL;DR: A uniqueness theorem is proven for the inverse problem of recovering the convolution kernel along with the boundary condition from the spectrum for a convolution integro-differential operator of the first order with a finite number of discontinuities.

TL;DR: In this article, an inverse spectral problem for the convolution integro-differential operator of fractional order > 2 is studied, and it is shown that specification of one spectrum determines such operator uniquely independently of particular value of $$\alpha > 2.

TL;DR: In this article, the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori is reduced to the solution of the so-called basic nonlinear integral equation with singularity.