EQUICONVERGENCE OF SOME COMPLEX INTERPOLATORY POLYNOMIALS

Walsh showed the close relation between the Lagrange interpolant in the nth roots of unity and the corresponding Taylor expansion for functions belonging to a certain class of analytic functions. Recent extensions of this phenomena to Hermite interpolation and other linear processes of interpolation have been surveyed in [3, 5]. Following a recent idea of L. Yuanren [7], we show how new relations between other linear operators can be derived which exhibit Walsh equiconvergence. © 1990 Springer-Verlag.