The operator of double differentiation, perturbed by the composition differentiation and a convolution one, on finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability recovering kernel from spectrum in weighted $L_2$-norm norm. For this purpose, we successively prove each step algorithm for solving inverse problem both norms. Besides justifying numerical co...

Recently, there appeared a considerable interest in inverse Sturm–Liouville-type problems with constant delay. However, necessary and sufficient conditions for solvability of such were obtained only one very particular situation. Here we address this gap by obtaining the case functional-differential pencils possessing more general form along nonlinear dependence on spectral parameter. For purpo...

Spectral problem for a self-adjoint third-order differential operator with non-local potential on finite interval is studied. Elementary functions that are analogues of sines and cosines such operators described. Direct inverse problems solved.

We solve the inverse spectral problem for rotationally symmetric manifolds, which include the class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the radius of rotation. An analogue of the Minkowski problem is also solved.