Geodesic
Subbotin's splines in the problem of extremal interpolation in the space $L_p$ for second-order linear differential operators
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 4, pp. 255-262

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For second-order linear differential operators $\mathcal L_2(D)$ of the form $D^2$, $D^2+\alpha^2$, $D^2-\beta^2$ $(\alpha,\beta>0)$, the Yanenko–Stechkin–Subbotin problem of extremal interpolation of numerical sequences by twice differentiable functions $f$ with the smallest value of the norm of the function $\mathcal L_2(D)f$ in the space $L_p$ $(1\le p\le \infty)$ is considered on a grid of nodes of the numerical axis that is infinite in both directions. Subbotin's parabolic splines and their analogs for the operators $D^2+\alpha^2$ and $D^2-\beta^2$ (with knots lying in the middle between consecutive interpolation nodes) are used to derive upper bounds for the values of the smallest norm in terms of grid steps for any value of $p$, $1\le p\le \infty$.
Keywords: Subbotin's splines, infinite grid, second-order differential operator.
Mots-clés : interpolation 
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     author = {V. T. Shevaldin},
     title = {Subbotin's splines in the problem of extremal interpolation in the space $L_p$ for second-order linear differential operators},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {255--262},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_4_a16/}
}
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V. T. Shevaldin. Subbotin's splines in the problem of extremal interpolation in the space $L_p$ for second-order linear differential operators. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 4, pp. 255-262. http://geodesic.mathdoc.fr/item/TIMM_2021_27_4_a16/