Geodesic
Extremal functional $L_p$-interpolation on an arbitrary mesh on the real axis
Sbornik. Mathematics, Tome 213 (2022) no. 4, pp. 556-577

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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 $p$. Bibliography: 13 titles.
Keywords: extremal interpolation, derivative, divided difference, spline, difference equation. 
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     title = {Extremal functional $L_p$-interpolation on an arbitrary mesh on the real axis},
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Yu. N. Subbotin; V. T. Shevaldin. Extremal functional $L_p$-interpolation on an arbitrary mesh on the real axis. Sbornik. Mathematics, Tome 213 (2022) no. 4, pp. 556-577. http://geodesic.mathdoc.fr/item/SM_2022_213_4_a5/