DISCRETE AND CONTINUOUS LIOUVILLE-GREEN-OLIVER APPROXIMATIONS - A UNIFIED TREATMENT VIA VOLTERRA-STIELTJES INTEGRAL-EQUATIONS

A unified treatment of the Liouville-Green-Olver approximation theory for linear second-order differential and difference equations is prese nted. This is based on reduction to Volterra-Stieltjes integral equati ons with respect to complex measures. The present approach embodies an d improves several previous results. Moreover, error bounds are obtain ed for recessive solutions of certain difference equations, for which only qualitative results were known. The theory can be applied, for in stance, to the asymptotics of certain families of orthogonal polynomia ls.