Determining of continuous delay in a spectral problem for Chebyshev operator of the first kind

A perturbed singular ordinary differential Chebyshev operator of the first kind with continuous delay is considered in this paper. For an arbitrary numerical sequence that does not differ much from eigenvalues sequence of an unperturbed operator, a problem is set to find the perturbation operator containing a continuous delay. A theorem of the existence of such an operator is being proved. An algorithm of finding the delay function in the form of a Fourier series is built and substantiated. The algorithm substantiation is based on the regularized traces theory.