Extremal problems, inequalities, and classical orthogonal polynomials

摘要

In this survey paper we give a short account on characterizations for very classical orthogonal polynomials via extremal problems and the corresponding inequalities. Besides the basic properties of the classical orthogonal polynomials, we consider polynomial inequalities of Landau and Kolmogoroff type, some weighted polynomial inequalities in L2-norm of Markov–Bernstein type, as well as the corresponding connections with the classical orthogonal polynomials.