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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - S. I. Novikov
TI  - Periodic interpolation with a minimum norm of the $m$-th derivative
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2006
SP  - 165
EP  - 172
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2006_9_2_a4/
LA  - ru
ID  - SJVM_2006_9_2_a4
ER  - 
%0 Journal Article
%A S. I. Novikov
%T Periodic interpolation with a minimum norm of the $m$-th derivative
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2006
%P 165-172
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2006_9_2_a4/
%G ru
%F SJVM_2006_9_2_a4
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/

[1] Tikhomirov V. M., Boyanov B. D., “O nekotorykh vypuklykh zadachakh teorii priblizhenii”, Serdika. B'lgarsko matematichesko spisanie, 5 (1979), 83–96 | MR | Zbl

[2] Bojanov B., “Favard's interpolation problem for periodic functions”, Fourier analysis and approximation theory, Vol. II (Budapest, August 16–21, 1976), Colloquia Mathematica Societatis J. Bolyai, 19, North-Holland Publishing Co., Amsterdam–New York, 1978, 161–173 | MR

[3] Subbotin Yu. N., “O svyazi mezhdu konechnymi raznostyami i sootvetstvuyuschimi proizvodnymi”, Trudy MIAN SSSR, 78, 1965, 24–42 | MR | Zbl

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

[5] Subbotin Yu. N., “Ekstremalnye zadachi teorii priblizheniya funktsii pri nepolnoi in- formatsii”, Trudy MIAN SSSR, 145, 1980, 152–168 | MR | Zbl

[6] Muir T., A treatise on the theory of determinants, Dover Publications Inc., New York, 1960 | MR

[7] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972 | MR | Zbl

[8] Golomb M., “Approximation by periodic spline interpolation on uniform meshes”, J. Approxim. Theory, 1:1 (1968), 26–65 | DOI | MR | Zbl

[9] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, T. 1, Nauka, M., 1970

[10] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1984

[11] Kurosh A. G., Kurs vysshei algebry, Nauka, M., 1971 | Zbl

[12] Berezin I. S., Zhidkov N. P., Metody vychislenii, T. 1, Fizmatgiz, M., 1959 | Zbl