V. A. Steklov's problem in the theory of orthogonal polynomials

One considers the asymptotic properties of orthogonal polynomials of various types depending on the properties and the singularities of the weight function and of the orthogonality line. One gives conditions for the boundedness of the orthogonal polynomials on some set or on the entire orthogonality line, asymptotic formulas for them, and various growth estimates in the case of singularities of the weight function and of the contour. One presents some methods for the investigation of the asymptotic properties of the orthogonal polynomials.