Geodesic
The Lebesgue constant of local cubic splines with equally-spaced knots
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 445-451.

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

It is proved that the uniform Lebesgue constant (the norm of a linear operator from $C$ to $C$) of local cubic splines with equally-spaced knots, which preserve cubic polynomials, is equal to $11/9$. 
@article{SJVM_2017_20_4_a7,
     author = {V. T. Shevaldin and O. Ya. Shevaldina},
     title = {The {Lebesgue} constant of local cubic splines with equally-spaced knots},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {445--451},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a7/}
}
TY  - JOUR
AU  - V. T. Shevaldin
AU  - O. Ya. Shevaldina
TI  - The Lebesgue constant of local cubic splines with equally-spaced knots
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2017
SP  - 445
EP  - 451
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a7/
LA  - ru
ID  - SJVM_2017_20_4_a7
ER  - 
%0 Journal Article
%A V. T. Shevaldin
%A O. Ya. Shevaldina
%T The Lebesgue constant of local cubic splines with equally-spaced knots
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2017
%P 445-451
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a7/
%G ru
%F SJVM_2017_20_4_a7
V. T. Shevaldin; O. Ya. Shevaldina. The Lebesgue constant of local cubic splines with equally-spaced knots. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 445-451. http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a7/

[1] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Metody splain-funktsii, Nauka, M., 1980 | MR

[2] Korneichuk N. P., Splainy v teorii priblizheniya, Nauka, M., 1984 | MR

[3] Shevaldin V. T., Approksimatsiya lokalnymi splainami, UrO RAN, Ekaterinburg, 2014

[4] Strelkova E. V., Shevaldin V. T., “On Lebesgue constants of local parabolic splines”, Proc. of the Steklov Institute of Mathematics, 289, suppl. 1 (2015), 192–198 | DOI | MR | Zbl

[5] Strelkova E. V., Shevaldin V. T., “On uniform Lebesgue constants of local exponential splines with equidistant knots”, Proc. of the Steklov Institute of Mathematics, 296, suppl. 1 (2017), 206–217 | DOI | MR

[6] Strelkova E. V., Shevaldin V. T., “O ravnomernykh konstantakh Lebega lokalnykh trigonometricheskikh splainov tretego poryadka”, Tr. Instituta matematiki i mekhaniki UrO RAN, 22, no. 2, 2016, 245–254 | DOI | MR

[7] Volkov Yu. S., Strelkova E. V., Shevaldin V. T., “Local approximation by splines with displacement of nodes”, Siberian Advances in Mathematics, 23:1 (2013), 63–75 | MR | Zbl

[8] Richards F., “Best bounds for the uniform periodic spline interpolation operator”, J. Approx. Theory, 7:3 (1973), 302–317 | DOI | MR | Zbl

[9] Volkov Yu. S., Subbotin Yu. N., “Fifty years of Schoenberg's problem on the convergence of spline interpolation”, Proc. of the Steklov Institute of Mathematics, 288, suppl. 1 (2015), 222–237 | DOI | MR