For citation:
Tyshkevich S. V., Shatalina A. V. Everywhere divergence of Lagrange processes on the unit circle. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 2, pp. 165-171. DOI: 10.18500/1816-9791-2014-14-2-165-171, EDN: SHHIEP
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
09.06.2014
Full text:
(downloads: 167)
Language:
Russian
Heading:
UDC:
517.538.7
EDN:
SHHIEP
Everywhere divergence of Lagrange processes on the unit circle
Autors:
Tyshkevich Sergey Viktorovich, Saratov State University
Shatalina Anna Vasilevna, Saratov State University
Abstract:
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.
Key words:
References:
- Smirnov V. I., Lebedev N. A. Functions of a Complex Variable: Constructive Theory. London, Iliffe Books Ltd., IX, 1968, 488 pp.
- Privalov A. A. Divergence of nterpolation processes on sets of the second category. Math. Notes, 1975, vol. 18, no. 2, pp. 692–694.
- Shatalina A. V. Divergence of Lagrange Processes on the Unit Circle. Dep. v VINITI [Dep. in VINITI], Saratov State University, no. 4060-В90, 19.07.1990, 30 p. (in Russian).
- K. Prachar. Raspredelenie prostyh chisel [The Distribution of Prime Numbers]. Мoscow, Mir, 1967. 513 p. (in Russian).
Received:
28.11.2014
Accepted:
15.04.2014
Published:
30.05.2014
Short text (in English):
(downloads: 70)
- 813 reads