Necessary Conditions forLpConvergence of Lagrange Interpolation on an Arbitrary System of Nodes Original Research Article

This paper gives powerful necessary conditions for convergence of Lagrange interpolation on an arbitrary system of nodes inLp(dα) withdαbelonging to the Szegőʹs class. This provides a partial answer to Problem XI of P. Turán [J. Approx. Theory29(1980), 33–34]. It is shown that in this case the asymptotics of distribution of the nodes must behave like the power asymptotics.