Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Tyshkevich S. V., Shatalina A. V. Everywhere divergence of Lagrange processes on the unit circle. Izv. Sarat. Univ. Math. Mech. Inform., 2014, vol. 14, iss. 2, pp. 165-171. DOI: 10.18500/1816-9791-2014-14-2-165-171

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: 56)
Language: 
Russian
Heading: 
UDC: 
517.538.7

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.

References: 
  1. Smirnov V. I., Lebedev N. A. Functions of a Complex Variable: Constructive Theory. London, Iliffe Books Ltd., IX, 1968, 488 pp.
  2. Privalov A. A. Divergence of nterpolation processes on sets of the second category. Math. Notes, 1975, vol. 18, no. 2, pp. 692–694.
  3. 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).
  4. K. Prachar. Raspredelenie prostyh chisel [The Distribution of Prime Numbers]. Мoscow, Mir, 1967. 513 p. (in Russian).
Short text (in English):
(downloads: 21)