Extremal functional -interpolation on an arbitrary mesh on the real axis

The Golomb-de Boor problem of extremal interpolation of infinite real sequences with smallest -norm of the th derivative of the interpolant, , on an arbitrary mesh on the real axis is studied under constraints on the norms of the corresponding divided differences. For this smallest norm, lower estimates are obtained for any in terms of -splines. For the second derivative, this quantity is estimated from below and above by constants depending on the parameter . Bibliography: 13 titles.