Method of Generalized Moment Representations in the Theory of Rational Approximation (A Survey)

Abstract

We give a survey of the method of generalized moment representations introduced by Dzyadyk in 1981 and its applications to Pade approximations. In particular, some properties of biorthogonal polynomials are investigated and numerous important examples are given. We also consider applications of this method to joint Pade approximations, Pade–Chebyshev approximations, Hermite–Pade approximations, and two-point Pade approximations.