Convergence of linear and nonlinear Padé approximants from series of orthogonal polynomials

Abstract

Analogues of the Nuttall-Pommerenke theorem and Wallin-type theorems for classical Padé approximants, are proved for linear and nonlinear Padé approximants formed from series of orthogonal polynomials, corresponding to a distribution d α ( x ) d\alpha (x) with at most finitely many sign changes.