On the divergence phenomenon in Hermite-Fejer interpolation

Generalizing results of L. Brutman and I. Gopengauz (1999, Constr,. Approx. 15, 611-617). we show that for any nonconstant entire function f and any i nterpolation scheme on [-1,1], the associated Hermite-Fejer interpolating p olynomials diverge on any infinite subset of C\[-1.1]. Moreover, it turns o ut that even for the locally uniform convergence on the open interval ]-1,1 [ it is necessary that the interpolation scheme converges to the arcsine di stribution. (C) 2000 Academic Press.