Apr 1, 1996
Journal of Approximation Theory
Abstract This paper gives powerful necessary conditions for convergence of Lagrange interpolation on an arbitrary system of nodes in L p ( dα ) with dα belonging to the Szego's class. This provides a partial answer to Problem XI of P. Turan [J. Approx. Theory 29 (1980), 33–34]. It is shown that in this case the asymptotics of distribution of the nodes must behave like the power asymptotics.