Cite this article as:
Tyshkevich S. ., Shatalina A. V. Everywhere divergence of Lagrange processes on the unit circle . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 2, pp. 165-171. DOI: https://doi.org/10.18500/1816-9791-2014-14-2-165-171
Language:
Russian
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UDC:
517.538.7
Everywhere divergence of Lagrange processes on the unit circle
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.
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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).
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