Geodesic
Extremal functional interpolation in the mean with least value of the $n$-th derivative for large averaging intervals
Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 114-132 
Yu. N. Subbotin. Extremal functional interpolation in the mean with least value of the $n$-th derivative for large averaging intervals. Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 114-132. http://geodesic.mathdoc.fr/item/MZM_1996_59_1_a10/
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     author = {Yu. N. Subbotin},
     title = {Extremal functional interpolation in the mean with least value of the $n$-th derivative for large averaging intervals},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1996},
     volume = {59},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_1_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The smallest number $A<\infty$ is found such that for any sequence $Y=\{y_k,k\in\mathbb Z\}$ with $|\Delta^ny_k|\le1$ there exists a $u(t)$, $|u(t)|\le A$, for which the equation $y^n(t)=u(t)$ ($-\infty) has a solution satisfying the conditions $$ y_k=\frac 1h\int_{-h/2}^{h/2}y(k+1)\,dt, $$ where $k\in\mathbb Z$, $1. A similar problem is treated in $L_p(-\infty,\infty)$. It is shown that for $h=2m$ ($m$ a natural number) no such finite $A$ exists.

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