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

The Golomb-de Boor problem of extremal interpolation of infinite real sequences with smallest $L_p$-norm of the $n$th derivative of the interpolant, $1\le p\le \infty$, 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 $n\in \mathbb N$ in terms of $B$-splines. For the second derivative, this quantity is estimated from below and above by constants depending on the parameter $p$.
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