Geodesic
Exact Lebesgue Constants for Interpolatory $\mathscr L$-Splines of Third Order
Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 59-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we obtain the Lebesgue constants for interpolatory $\mathscr L$-splines of third order with uniform nodes, i.e., the norms of interpolation operators from $\mathrm C$ to $\mathrm C$ describing the process of interpolation of continuous bounded and continuous periodic functions by $\mathscr L$-splines of third order with uniform nodes on the real line. As a corollary, we obtain exact Lebesgue constants for interpolatory polynomial parabolic splines with uniform nodes.
Mots-clés : Lebesgue constant
Keywords: interpolatory $\mathscr L$-spline, $B$-spline, polynomial parabolic spline with uniform nodes, continuous bounded function, continuous periodic function. 
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V. A. Kim. Exact Lebesgue Constants for Interpolatory $\mathscr L$-Splines of Third Order. Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 59-68. http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a4/

[1] F. Schurer, E. W. Cheney, “On interpolating cubic splines with equally-spaced nodes”, Nederl. Akad. Wetensch. Proc. Ser. A, 71:5 (1968), 517–524 | MR | Zbl

[2] F. Richards, “The Lebesgue constants for cardinal spline interpolation”, J. Approximation Theory, 14:2 (1975), 83–92 | DOI | MR | Zbl

[3] Yu. N. Subbotin, S. A. Telyakovskii, “Asimptotika konstant Lebega periodicheskikh interpolyatsionnykh splainov s ravnootstoyaschimi uzlami”, Matem. sb., 191:8 (2000), 131–140 | MR | Zbl

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

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