Geodesic
A Criterion for the Uniform Convergence of the Lagrange–Jacobi Interpolation Process
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 254-266 
V. V. Novikov. A Criterion for the Uniform Convergence of the Lagrange–Jacobi Interpolation Process. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 254-266. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/
@article{MZM_2006_79_2_a8,
     author = {V. V. Novikov},
     title = {A~Criterion for the {Uniform} {Convergence} of the {Lagrange{\textendash}Jacobi} {Interpolation} {Process}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {254--266},
     year = {2006},
     volume = {79},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/}
}
TY  - JOUR
AU  - V. V. Novikov
TI  - A Criterion for the Uniform Convergence of the Lagrange–Jacobi Interpolation Process
JO  - Matematičeskie zametki
PY  - 2006
SP  - 254
EP  - 266
VL  - 79
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/
LA  - ru
ID  - MZM_2006_79_2_a8
ER  - 
%0 Journal Article
%A V. V. Novikov
%T A Criterion for the Uniform Convergence of the Lagrange–Jacobi Interpolation Process
%J Matematičeskie zametki
%D 2006
%P 254-266
%V 79
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/
%G ru
%F MZM_2006_79_2_a8

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

We obtain a uniform and sufficient condition for the convergence of the Lagrange interpolation process with Jacobi nodes on a closed interval $[a,b]\subset(-1,1)$. The condition is stated in terms of the second differences of the interpolated function and uses its values only at the interpolation nodes. Some well-known criteria for uniform convergence are obtained as a consequence of our result.

[1] Geronimus Ya. L., “O skhodimosti interpolyatsionnogo protsessa Lagranzha s uzlami v kornyakh ortogonalnykh mnogochlenov”, Izv. AN SSSR. Ser. matem., 27 (1963), 529–560 | MR | Zbl

[2] Nevai G. P., “Zamechaniya ob interpolirovanii”, Acta Math. Sci. Hungar., 25 (1974), 123–144 | DOI | MR | Zbl

[3] Pilipchuk S. S., “O priznakakh skhodimosti interpolyatsionnykh protsessov”, Izv. vuzov. Matem., 1979, no. 12, 39–44 | MR | Zbl

[4] Privalov A. A., Teoriya interpolirovaniya funktsii, Izd-vo Saratovskogo un-ta, Saratov, 1990 | MR

[5] Privalov A. A., “O ravnomernoi skhodimosti interpolyatsionnykh protsessov Lagranzha”, Matem. zametki, 39:2 (1986), 228–244 | MR | Zbl

[6] Privalov A. A., “Kriterii ravnomernoi skhodimosti interpolyatsionnykh protsessov Lagranzha”, Izv. vuzov. Matem., 1986, no. 5, 49–59 | MR

[7] Erdős P., Grünwald G., “Über einen Faber'schen Satz”, Ann. of Math., 39 (1938), 257–261 | DOI | MR | Zbl

[8] Novikov V. V., “O raskhodimosti ryada Fure funktsii so skhodyaschimsya interpolyatsionnym protsessom Lagranzha”, Analysis Math., 29 (2003), 289–317 | DOI | MR | Zbl

[9] Segë G., Ortogonalnye mnogochleny, Fizmatlit, M., 1962