Geodesic
Everywhere divergence of Lagrange processes on the unit circle
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 165-171 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the convergence of Lagrange interpolation processes in the closed unit disk. Choosing a matrix with a certain distribution of interpolation nodes allowed to construct the set, completely covering the unit circle, and the function for which the process diverges everywhere on this set. 
@article{ISU_2014_14_2_a6,
     author = {S. V. Tyshkevich and A. V. Shatalina},
     title = {Everywhere divergence of {Lagrange} processes on the unit circle},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {165--171},
     year = {2014},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a6/}
}
TY  - JOUR
AU  - S. V. Tyshkevich
AU  - A. V. Shatalina
TI  - Everywhere divergence of Lagrange processes on the unit circle
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 165
EP  - 171
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a6/
LA  - ru
ID  - ISU_2014_14_2_a6
ER  - 
%0 Journal Article
%A S. V. Tyshkevich
%A A. V. Shatalina
%T Everywhere divergence of Lagrange processes on the unit circle
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 165-171
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a6/
%G ru
%F ISU_2014_14_2_a6
S. V. Tyshkevich; A. V. Shatalina. Everywhere divergence of Lagrange processes on the unit circle. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 165-171. http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a6/

[1] Smirnov V. I., Lebedev N. A., Functions of a Complex Variable: Constructive Theory, Iliffe Books Ltd., London, 1968, 488 pp. | MR | MR | Zbl

[2] Privalov A. A., “Divergence of nterpolation processes on sets of the second category”, Math. Notes, 18:2 (1975), 692–694 | DOI | MR | Zbl

[3] Shatalina A. V., Divergence of Lagrange Processes on the Unit Circle, Dep. in VINITI 19.07.1990, No 4060-B90, Saratov State University, 30 pp.

[4] Prachar K., The Distribution of Prime Numbers, Mir, Moscow, 1967, 513 pp. | MR