Geodesic
Periodic interpolation with a minimum norm of the $m$-th derivative
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 2, pp. 165-172

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In this paper, the interpolation problem for periodic data with a bounded lp-norm is investigated for an interpolating set of smooth periodic functions. In the cases when $p=2$ and $p=\infty$, the exact values of the $L_p$-norms of the $m$-th derivative of the best interpolants are found for a certain class of sequences. 
@article{SJVM_2006_9_2_a4,
     author = {S. I. Novikov},
     title = {Periodic interpolation with a minimum norm of the $m$-th derivative},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {165--172},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_2_a4/}
}
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S. I. Novikov. Periodic interpolation with a minimum norm of the $m$-th derivative. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 2, pp. 165-172. http://geodesic.mathdoc.fr/item/SJVM_2006_9_2_a4/