Sturm–Liouville?type operators with frozen argument and Chebyshev polynomials

In recent years, there appeared a growing interest in the inverse spectral theory for functional-differential operators with frozen argument. Such are nonlocal and belong to so-called loaded differential operators, which frequently appear mathematics as well natural sciences engineering. However, various classes of classical methods not applicable. For this reason, it is relevant develop new approaches solving problems type. We establish deep connection between problem argument Chebyshev polynomials first second kinds. Appearing be an from point view itself, gives perspective method studying particular, allows one completely describe all non-degenerate degenerate cases, that is, when corresponding uniquely solvable or not, respectively. Moreover, convenient description isospectral potentials case, demonstrated by some illustrative examples.