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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Extremal functional interpolation in the mean with least value of the $n$-th derivative for large averaging intervals},
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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/

[1] Subbotin Yu. N., “Funktsionalnaya interpolyatsiya v srednem s naimenshei $n$-i proizvodnoi”, Tr. MIAN, 88, Nauka, M., 1967, 30–60 | MR | Zbl

[2] Subbotin Yu. N., “Ekstremalnye zadachi funktsionalnoi interpolyatsii i interpolyatsionnye v srednem splainy”, Tr. MIAN, 138, Nauka, M., 1975, 118–173 | MR | Zbl

[3] Sharma A., Tsimbalario I., “Nekotorye lineinye differentsialnye operatory i obobschennye raznosti”, Matem. zametki, 21:2 (1977), 161–172 | MR | Zbl

[4] Shevaldin V. T., “Ob odnoi zadache funktsionalnoi interpolyatsii”, Matem. zametki, 29:4 (1981), 603–622 | MR | Zbl

[5] Shevaldin V. T., “Nekotorye zadachi ekstremalnoi interpolyatsii v srednem dlya lineinykh differentsialnykh operatorov”, Tr. MIAN, 164, Nauka, M., 1983, 203–240 | MR | Zbl

[6] Stechkin S. B., Subbotin Yu. N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | Zbl