Geodesic
Direct and inverse theorems on approximation by piecewise polynomial functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 129-144.

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

The paper is concerned with some characteristics of approximation by piecewise polynomial functions with nonfixed knots in various integral metrics $L_p[a,b]$, $0$. 
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A. S. Kochurov. Direct and inverse theorems on approximation by piecewise polynomial functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 129-144. http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a6/

[1] Brudnyi Yu. A., “Adaptivnaya approksimatsiya funktsii s osobennostyami”, Tr. MMO, 55, 1994, 149–242 | MR | Zbl

[2] Stechkin S. B., “Odna optimizatsionnaya zadacha”, Numerische Methoden der Approximationtheorie, v. I, Birkhäuser, Basel, 1972, 205–208 | DOI

[3] Chanturiya Z. A., “Modul izmeneniya funktsii i ego primenenie v teorii ryadov Fure”, Dokl. AN SSSR, 214:1 (1974), 63–66 | Zbl

[4] Bennett G., Grosse-Erdmann K.-G., “Weighted Hardy inequalities for decreasing sequences and functions”, Math. Ann., 334 (2006), 489–531 | DOI | MR | Zbl

[5] Kufner A., Persson L.-E., Weighted Inequalities of Hardy Type, World Scientific, 2003 | MR | Zbl

[6] Popov V. A., “On the connection between rational and spline approximation”, C. R. Acad. Bulgare Sci., 27:5 (1974), 623–626 | MR | Zbl

[7] Popov V. A., Sendov Bl. Kh., “Classes characterized by best-possible approximation by spline functions”, Math. Notes, 8:2 (1970), 550–557 | DOI | MR | Zbl